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searching for Factorization 163 found (1916 total)

alternate case: factorization

Symmetric matrix (2,812 words) [view diff] exact match in snippet view article find links to article

non-negative entries. This result is referred to as the Autonne–Takagi factorization. It was originally proved by Léon Autonne (1915) and Teiji Takagi (1925)

Gram–Schmidt process (4,423 words) [view diff] no match in snippet view article find links to article

In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a way of finding a set of two

QR decomposition (5,100 words) [view diff] exact match in snippet view article find links to article

In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of

Numerical linear algebra (2,766 words) [view diff] exact match in snippet view article find links to article

decompositions like the singular value decomposition, the QR factorization, the LU factorization, or the eigendecomposition, which can then be used to answer

Primorial (1,561 words) [view diff] no match in snippet view article find links to article

Look up -ial in Wiktionary, the free dictionary. In mathematics, and more particularly in number theory, primorial, denoted by "pn#", is a function from

Hardy space (4,038 words) [view diff] exact match in snippet view article find links to article

function, as defined below (Rudin 1987, Thm 17.17). This "Beurling factorization" allows the Hardy space to be completely characterized by the spaces

Riemann–Hilbert problem (3,712 words) [view diff] exact match in snippet view article find links to article

infinite self-intersection in the complex plane), a Riemann–Hilbert factorization problem is the following. Given a matrix function G ( t ) {\displaystyle

Up to (846 words) [view diff] exact match in snippet view article find links to article

condition or transformation. For example, the statement "an integer's prime factorization is unique up to ordering" is a concise way to say that any two lists

Googolplex (834 words) [view diff] exact match in snippet view article find links to article

10100 zeroes; that is, a 1 followed by a googol of zeroes. Its prime factorization is 2googol ×5googol. In 1920, Edward Kasner's nine-year-old nephew,

Rational root theorem (1,527 words) [view diff] exact match in snippet view article find links to article

a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials. The integral root theorem is the special case of the

Ordinal arithmetic (4,965 words) [view diff] exact match in snippet view article find links to article

the unique factorization theorem: every nonzero ordinal can be written as a product of a finite number of prime ordinals. This factorization into prime

Löschian number (302 words) [view diff] exact match in snippet view article find links to article

They are a set of whole numbers, including zero, and having prime factorization in which all primes congruent to 2 mod 3 have even powers (there is

Hilbert's paradox of the Grand Hotel (2,131 words) [view diff] exact match in snippet view article find links to article

for the first coach, etc.). Because every number has a unique prime factorization, it is easy to see all people will have a room, while no two people

Cyclotomic field (2,107 words) [view diff] exact match in snippet view article find links to article

{\displaystyle n} )—and more precisely, because of the failure of unique factorization in their rings of integers—that Ernst Kummer first introduced the concept

Ladder operator (4,537 words) [view diff] exact match in snippet view article find links to article

\omega ^{2}r^{2}.} It can similarly be managed using the factorization method. A suitable factorization is given by C l = p r + i ℏ ( l + 1 ) r − i μ ω r {\displaystyle

Wiener–Hopf method (1,530 words) [view diff] no match in snippet view article find links to article

The Wiener–Hopf method is a mathematical technique widely used in applied mathematics. It was initially developed by Norbert Wiener and Eberhard Hopf as

Strain partitioning (1,401 words) [view diff] exact match in snippet view article find links to article

terranes for several hundred kilometers parallel to the orogen. Strain factorization is a mathematical approach to quantify and characterize the variation

Doob–Dynkin lemma (566 words) [view diff] exact match in snippet view article find links to article

lemma, named after Joseph L. Doob and Eugene Dynkin (also known as the factorization lemma), characterizes the situation when one random variable is a function

Markov random field (2,817 words) [view diff] exact match in snippet view article find links to article

graph is chordal (by equivalence to a Bayesian network) When such a factorization does exist, it is possible to construct a factor graph for the network

Hurwitz quaternion (1,242 words) [view diff] exact match in snippet view article find links to article

quaternion can be factored as a product of irreducible quaternions. This factorization is not in general unique, even up to units and order, because a positive

Almost prime (402 words) [view diff] exact match in snippet view article find links to article

if Ω(n) = k, where Ω(n) is the total number of primes in the prime factorization of n (can be also seen as the sum of all the primes' exponents): Ω (

Multiplicative partition (1,101 words) [view diff] exact match in snippet view article find links to article

In number theory, a multiplicative partition or unordered factorization of an integer n {\displaystyle n} is a way of writing n {\displaystyle n} as a

Arne Beurling (935 words) [view diff] exact match in snippet view article find links to article

harmonic analysis, complex analysis and potential theory. The "Beurling factorization" helped mathematical scientists to understand the Wold decomposition

Model category (2,402 words) [view diff] exact match in snippet view article find links to article

{\displaystyle (C\cap W,F)} is a weak factorization system, ( C , F ∩ W ) {\displaystyle (C,F\cap W)} is a weak factorization system W {\displaystyle W} satisfies

Quadratic field (1,306 words) [view diff] exact match in snippet view article find links to article

rings, the ideal class number, which measures the failure of unique factorization, is given in OEIS A003649; for the imaginary case, they are given in

Niven's constant (275 words) [view diff] exact match in snippet view article find links to article

named after Ivan Niven, is the largest exponent appearing in the prime factorization of any natural number n "on average". More precisely, if we define H(1)

Monoid factorisation (688 words) [view diff] exact match in snippet view article find links to article

j += 1 while i <= k: factorization.append(s[i:i + j - k]) i += j - k return factorization The Hall set provides a factorization. Indeed, Lyndon words

NP (complexity) (2,784 words) [view diff] exact match in snippet view article

problem in polynomial time. The decision problem version of the integer factorization problem: given integers n and k, is there a factor f with 1 < f < k

Amenable number (405 words) [view diff] exact match in snippet view article find links to article

are available, one can always obtain a solution by taking the prime factorization (expressed with repeated factors rather than exponents) and add as many

Stinespring dilation theorem (2,113 words) [view diff] exact match in snippet view article find links to article

mathematics, Stinespring's dilation theorem, also called Stinespring's factorization theorem, named after W. Forrest Stinespring, is a result from operator

Googol (1,254 words) [view diff] exact match in snippet view article find links to article

duotrigintillion (short scale) or ten sexdecilliard (long scale). Its prime factorization is 2100 × 5100. The term was coined in 1920 by 9-year-old Milton Sirotta

Septimal comma (480 words) [view diff] exact match in snippet view article find links to article

interval in just intonation that contains the number seven in its prime factorization. There is more than one such interval, so the term septimal comma is

Maris–McGwire–Sosa pair (236 words) [view diff] exact match in snippet view article find links to article

digits of its prime factorization gives the same sum. Thus 61 → 6 + 1 (the sum of its digits) + 6 + 1 (since 61 is its prime factorization) and 62 → 6 + 2

Bruun's FFT algorithm (2,138 words) [view diff] exact match in snippet view article find links to article

transform (FFT) algorithm based on an unusual recursive polynomial-factorization approach, proposed for powers of two by G. Bruun in 1978 and generalized

Solving quadratic equations with continued fractions (1,766 words) [view diff] no match in snippet view article find links to article

In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is a x 2 + b x + c = 0 , {\displaystyle ax^{2}+bx+c=0

List of Lehigh University engineering highlights (1,210 words) [view diff] exact match in snippet view article find links to article

Dodson, whose significant contributions to cryptography led to the factorization of RSA-140 and RSA-155 on an SGI Origin based supercomputer in 1999

Free monoid (2,985 words) [view diff] exact match in snippet view article find links to article

theorem states that the Lyndon words furnish a factorization. More generally, Hall words provide a factorization; the Lyndon words are a special case of the

P-adic valuation (1,380 words) [view diff] exact match in snippet view article find links to article

_{p}(n)} is the exponent to which p {\displaystyle p} appears in the prime factorization of n {\displaystyle n} . The p-adic valuation is a valuation and gives

Bairstow's method (1,216 words) [view diff] no match in snippet view article find links to article

In numerical analysis, Bairstow's method is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree. The algorithm first

Ruffini's rule (1,208 words) [view diff] exact match in snippet view article find links to article

simpler method.) A typical example, where one needs the quotient, is the factorization of a polynomial p ( x ) {\displaystyle p(x)} for which one knows a root

Bairstow's method (1,216 words) [view diff] no match in snippet view article find links to article

In numerical analysis, Bairstow's method is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree. The algorithm first

The Whetstone of Witte (436 words) [view diff] exact match in snippet view article find links to article

indices and surds larger than 3 in a systematic form based on the prime factorization of the exponent: a factor of two he termed a zenzic, and a factor of

Cofibration (1,643 words) [view diff] exact match in snippet view article find links to article

cofibrations and weak equivalences satisfying certain lifting and factorization axioms. In what follows, let I = [ 0 , 1 ] {\displaystyle I=[0,1]} denote

Splitting circle method (2,184 words) [view diff] exact match in snippet view article find links to article

splitting circle method is a numerical algorithm for the numerical factorization of a polynomial and, ultimately, for finding its complex roots. It was

Lyndon word (2,749 words) [view diff] exact match in snippet view article find links to article

suffix of the given string. A factorization into a nonincreasing sequence of Lyndon words (the so-called Lyndon factorization) can be constructed in linear

Expectation propagation (275 words) [view diff] exact match in snippet view article find links to article

probability distribution. It uses an iterative approach that uses the factorization structure of the target distribution. It differs from other Bayesian

CoCoA (361 words) [view diff] exact match in snippet view article find links to article

of zero-dimensional schemes, Poincaré series and Hilbert functions, factorization of polynomials, and toric ideals. The capabilities of CoCoA and the

Graeffe's method (2,048 words) [view diff] exact match in snippet view article find links to article

type is straightforward, whereas addition is performed following the factorization c 3 = c 1 + c 2 = | c 1 | ⋅ ( α 1 + α 2 | c 2 | | c 1 | ) {\displaystyle

Inverse scattering transform (2,604 words) [view diff] exact match in snippet view article find links to article

: 72 The inverse scattering problem is equivalent to a Riemann–Hilbert factorization problem, at least in the case of equations of one space dimension. This

Kevin Costello (516 words) [view diff] exact match in snippet view article find links to article

recent work on formalism for quantum field theory uses the idea of a factorization algebra to describe the local structure of quantum observables, such

Well-ordering principle (1,184 words) [view diff] exact match in snippet view article find links to article

as a product of primes. This theorem constitutes part of the Prime Factorization Theorem. Proof (by well-ordering principle). Let C {\displaystyle C}

Fast Library for Number Theory (157 words) [view diff] no match in snippet view article find links to article

The Fast Library for Number Theory (FLINT) is a C library for number theory applications. The two major areas of functionality currently implemented in

Computational complexity theory (6,704 words) [view diff] exact match in snippet view article find links to article

Notable examples include the traveling salesman problem and the integer factorization problem. It is tempting to think that the notion of function problems

Square root of a matrix (4,651 words) [view diff] exact match in snippet view article find links to article

square root may be used for any factorization of a positive semidefinite matrix A as BTB = A, as in the Cholesky factorization, even if BB ≠ A. This distinct

Derek Atkins (113 words) [view diff] exact match in snippet view article find links to article

co-authored the paper The Magic Words are Squeamish Ossifrage detailing the factorization of RSA-129. "Derek Atkins Joins SecureRF as Chief Technology Officer"

Bayesian network (6,630 words) [view diff] exact match in snippet view article find links to article

modeled by a Bayesian network are encoded by a DAG (according to the factorization and Markov properties above), its marginal independence statements—the

Prime signature (397 words) [view diff] exact match in snippet view article find links to article

multiset of (nonzero) exponents of its prime factorization. The prime signature of a number having prime factorization p 1 m 1 p 2 m 2 … p n m n {\displaystyle

Skolem arithmetic (1,957 words) [view diff] exact match in snippet view article find links to article

(Prime(p) → ∃P.(InvAdicAbs(p, n, P) ∧ InvAdicAbs(p, m, P)))) [Unique factorization] ∀p.∀n.∀m.(Prime(p) → ∃P.∃Q.(InvAdicAbs(p, n, P) ∧ InvAdicAbs(p, m,

HHL algorithm (4,990 words) [view diff] no match in snippet view article find links to article

The Harrow–Hassidim–Lloyd (HHL) algorithm is a quantum algorithm for numerically solving a system of linear equations, designed by Aram Harrow, Avinatan

Lambert series (3,873 words) [view diff] exact match in snippet view article find links to article

recently published over 2017–2018 relates to so-termed Lambert series factorization theorems of the form ∑ n ≥ 1 a n q n 1 ± q n = 1 ( ∓ q ; q ) ∞ ∑ n ≥

Cycle rank (1,221 words) [view diff] exact match in snippet view article find links to article

computations, namely for using nested dissection to compute the Cholesky factorization of a (symmetric) matrix in parallel. A given sparse ( n × n ) {\displaystyle

Laguerre's method (1,776 words) [view diff] no match in snippet view article find links to article

In numerical analysis, Laguerre's method is a root-finding algorithm tailored to polynomials. In other words, Laguerre's method can be used to numerically

Chen Chung Chang (198 words) [view diff] exact match in snippet view article find links to article

He obtained his PhD from Berkeley in 1955 on "Cardinal and Ordinal Factorization of Relation Types" under Alfred Tarski. He wrote the standard text Chang

Linda Preiss Rothschild (498 words) [view diff] exact match in snippet view article find links to article

but subsequently her interests broadened to include also polynomial factorization, partial differential equations, harmonic analysis, and the theory of

Square root of 2 (6,131 words) [view diff] exact match in snippet view article find links to article

a^{2}=2b^{2}} . Being the same quantity, each side has the same prime factorization by the fundamental theorem of arithmetic, and in particular, would have

Chiral algebra (510 words) [view diff] exact match in snippet view article find links to article

{\displaystyle T} of translations. Chiral algebras can also be reformulated as factorization algebras. Chiral homology Chiral Lie algebra Beilinson, Alexander; Drinfeld

Budan's theorem (2,241 words) [view diff] no match in snippet view article find links to article

In mathematics, Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number

Image (category theory) (1,822 words) [view diff] exact match in snippet view article

I\to I'} such that m = m ′ v {\displaystyle m=m'\,v} . Remarks: such a factorization does not necessarily exist. e {\displaystyle e} is unique by definition

Unitary matrix (1,331 words) [view diff] exact match in snippet view article find links to article

− δ , {\displaystyle \ \beta =\psi -\delta \ ,} has the following factorization: U = e i φ / 2 [ e i ψ 0 0 e − i ψ ] [ cos ⁡ θ sin ⁡ θ − sin ⁡ θ cos

DiVincenzo's criteria (1,819 words) [view diff] exact match in snippet view article find links to article

implement quantum algorithms such as Grover's search algorithm or Shor factorization. The first five conditions regard quantum computation itself. Two additional

GloVe (1,590 words) [view diff] exact match in snippet view article find links to article

combines the features of two model families, namely the global matrix factorization and local context window methods. It is developed as an open-source

Ruth–Aaron pair (627 words) [view diff] exact match in snippet view article find links to article

depending on how many times to count primes that appear multiple times in a factorization. The name was given by Carl Pomerance for Babe Ruth and Hank Aaron,

Weierstrass preparation theorem (1,218 words) [view diff] exact match in snippet view article find links to article

are also a number of variants of the theorem, that extend the idea of factorization in some ring R as u·w, where u is a unit and w is some sort of distinguished

Hall word (3,281 words) [view diff] exact match in snippet view article find links to article

this "backwardness" is what provides the descending order required for factorization. Reversing the inequality does not reverse this "backwardness". Consider

Casio ClassPad 300 (1,240 words) [view diff] exact match in snippet view article find links to article

input of expressions, and displays them as they appear in a textbook. Factorization of expressions, calculation of limit values of functions, and other

DiVincenzo's criteria (1,819 words) [view diff] exact match in snippet view article find links to article

implement quantum algorithms such as Grover's search algorithm or Shor factorization. The first five conditions regard quantum computation itself. Two additional

Harish-Chandra module (378 words) [view diff] exact match in snippet view article find links to article

then its Harish-Chandra module is a representation with desirable factorization properties. Let G be a Lie group and K a compact subgroup of G. If (

Jenkins–Traub algorithm (3,635 words) [view diff] exact match in snippet view article find links to article

deflated by dividing off the corresponding linear factor. Indeed, the factorization of the polynomial into the linear factor and the remaining deflated

Bonse's inequality (170 words) [view diff] exact match in snippet view article find links to article

a primorial to the smallest prime that does not appear in its prime factorization. It states that if p1, ..., pn, pn+1 are the smallest n + 1 prime numbers

Durand–Kerner method (3,080 words) [view diff] no match in snippet view article find links to article

In numerical analysis, the Weierstrass method or Durand–Kerner method, discovered by Karl Weierstrass in 1891 and rediscovered independently by Durand

Aberth method (1,288 words) [view diff] exact match in snippet view article find links to article

z_{n}^{*}} , the roots of p ( x ) {\displaystyle p(x)} , that give the factorization: p ( x ) = p n ⋅ ( x − z 1 ∗ ) ⋅ ( x − z 2 ∗ ) ⋯ ( x − z n ∗ ) . {\displaystyle

Uniqueness theorem (332 words) [view diff] exact match in snippet view article find links to article

division. Fundamental theorem of arithmetic, the uniqueness of prime factorization. Holmgren's uniqueness theorem for linear partial differential equations

Rigorous coupled-wave analysis (1,025 words) [view diff] exact match in snippet view article find links to article

harmonics can also slow convergence and techniques like fast Fourier factorization (FFF) should be used. FFF is straightforward to implement for 1D gratings

Hall subgroup (814 words) [view diff] exact match in snippet view article find links to article

The easiest way to find the Hall divisors is to write the prime power factorization of the number in question and take any subset of the factors. For example

P-adic number (7,716 words) [view diff] exact match in snippet view article find links to article

method that allows to "lift" the factorization modulo p of a polynomial with integer coefficients to a factorization modulo p n {\textstyle p^{n}} for

Zappa–Szép product (1,290 words) [view diff] exact match in snippet view article find links to article

the Zappa–Rédei–Szép product, general product, knit product, exact factorization or bicrossed product) describes a way in which a group can be constructed

Ideal number (1,225 words) [view diff] exact match in snippet view article find links to article

the nonprincipal ideal. Kummer first published the failure of unique factorization in cyclotomic fields in 1844 in an obscure journal; it was reprinted

P versus NP problem (7,784 words) [view diff] exact match in snippet view article find links to article

quasi-polynomial time. The integer factorization problem is the computational problem of determining the prime factorization of a given integer. Phrased as

Harm Bart (423 words) [view diff] exact match in snippet view article find links to article

the Erasmus University Rotterdam, particularly known for his work on "factorization problems for matrix and operator functions." Born in Enkhuizen, Bart

Operator theory (1,638 words) [view diff] exact match in snippet view article find links to article

bounded linear operator A between complex Hilbert spaces is a canonical factorization as the product of a partial isometry and a non-negative operator. The

John C. Collins (564 words) [view diff] exact match in snippet view article find links to article

contributed to the formulation of factorization proofs for exclusive processes and he provided a proof of factorization for hard high-energy diffraction

Encyclopedia of Cryptography and Security (217 words) [view diff] exact match in snippet view article find links to article

authentication and identification, copy protection, cryptoanalysis and security, factorization algorithms and primality tests, cryptographic protocols, key management

Matrix analysis (1,133 words) [view diff] no match in snippet view article find links to article

In mathematics, particularly in linear algebra and applications, matrix analysis is the study of matrices and their algebraic properties. Some particular

Operator theory (1,638 words) [view diff] exact match in snippet view article find links to article

bounded linear operator A between complex Hilbert spaces is a canonical factorization as the product of a partial isometry and a non-negative operator. The

Harm Bart (423 words) [view diff] exact match in snippet view article find links to article

the Erasmus University Rotterdam, particularly known for his work on "factorization problems for matrix and operator functions." Born in Enkhuizen, Bart

David William Boyd (458 words) [view diff] exact match in snippet view article find links to article

analysis, inequalities related to geometry, number theory, and polynomial factorization, sphere packing, number theory involving Diophantine approximation and

Leopold Infeld (778 words) [view diff] exact match in snippet view article find links to article

Max Born and Leopold Infeld, who first proposed it. The Infeld-Hull Factorization Method describing general sets of solutions to the Schrödinger equation

John C. Collins (564 words) [view diff] exact match in snippet view article find links to article

contributed to the formulation of factorization proofs for exclusive processes and he provided a proof of factorization for hard high-energy diffraction

George Sterman (379 words) [view diff] exact match in snippet view article find links to article

method in that regime. He also worked on reformulation and proof of factorization theorems with Stephen Libby, John C. Collins and Davison E. Soper. He

Strong prime (767 words) [view diff] exact match in snippet view article find links to article

should be chosen as the product of two strong primes. This makes the factorization of n = pq using Pollard's p − 1 algorithm computationally infeasible

Heegner number (3,525 words) [view diff] exact match in snippet view article find links to article

] {\displaystyle \mathbb {Q} \left[{\sqrt {-d}}\right]} has unique factorization. The determination of such numbers is a special case of the class number

Dc (computer program) (2,646 words) [view diff] exact match in snippet view article

3, 2019. "Advanced Bash-Scripting Guide, Chapter 16, Example 16-52 (Factorization)". Retrieved 2020-09-20. Adam Back. "Diffie–Hellman in 2 lines of Perl"

Ridge regression (4,146 words) [view diff] exact match in snippet view article find links to article

then given as a factorization of the matrix Q = Γ T Γ {\displaystyle Q=\Gamma ^{\mathsf {T}}\Gamma } (e.g. the Cholesky factorization) and is considered

Mehrotra predictor–corrector method (1,729 words) [view diff] exact match in snippet view article find links to article

compute the Cholesky decomposition (factorization) of a large matrix to find the search direction. The factorization step is the most computationally expensive

Function problem (1,174 words) [view diff] exact match in snippet view article find links to article

integer factorization problem is not self-reducible, because deciding whether an integer is prime is in P (easy), while the integer factorization problem

Monic polynomial (1,159 words) [view diff] exact match in snippet view article find links to article

associated to a unique monic polynomial. In particular, the unique factorization property of polynomials can be stated as: Every polynomial can be uniquely

Post-quantum cryptography (6,408 words) [view diff] exact match in snippet view article find links to article

on the difficulty of one of three mathematical problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve discrete

Mehrotra predictor–corrector method (1,729 words) [view diff] exact match in snippet view article find links to article

compute the Cholesky decomposition (factorization) of a large matrix to find the search direction. The factorization step is the most computationally expensive

Monic polynomial (1,159 words) [view diff] exact match in snippet view article find links to article

associated to a unique monic polynomial. In particular, the unique factorization property of polynomials can be stated as: Every polynomial can be uniquely

3D reconstruction from multiple images (3,002 words) [view diff] exact match in snippet view article find links to article

method was proposed by Tomasi and Kanade, in which they used an affine factorization approach to extract 3D from image sequences. However, the assumption

Selberg class (1,908 words) [view diff] exact match in snippet view article find links to article

primitive functions. Selberg's conjectures, described below, imply that the factorization into primitive functions is unique. Examples of primitive functions

Derrick Norman Lehmer (533 words) [view diff] exact match in snippet view article find links to article

continued to teach there until retiring in 1937. In 1903, he presented a factorization of Jevons's number (8,616,460,799) at the San Francisco Section of the

Redheffer matrix (6,249 words) [view diff] exact match in snippet view article find links to article

(2017) develops a factorization-theorem-like treatment to expanding these sums which is an analog to the Lambert series factorization results given in

Cluster-expansion approach (2,121 words) [view diff] exact match in snippet view article find links to article

{S} }} is the singlet factorization of an N {\displaystyle N} -particle expectation value. Physically, the singlet factorization among Fermions produces

Symmetric space (4,599 words) [view diff] exact match in snippet view article find links to article

B\right|_{{\mathfrak {m}}_{d}}} In certain practical applications, this factorization can be interpreted as the spectrum of operators, e.g. the spectrum of

Polynomial root-finding (4,030 words) [view diff] exact match in snippet view article find links to article

the polynomial and its derivative. The square-free factorization of a polynomial p is a factorization p = p 1 p 2 2 ⋯ p k k {\displaystyle p=p_{1}p_{2}^{2}\cdots

Pierre Samuel (569 words) [view diff] exact match in snippet view article find links to article

émérite at the Université Paris-Sud (Orsay). His lectures on unique factorization domains published by the Tata Institute of Fundamental Research played

Structure theorem for finitely generated modules over a principal ideal domain (2,160 words) [view diff] exact match in snippet view article find links to article

uniquely decomposed in much the same way that integers have a prime factorization. The result provides a simple framework to understand various canonical

Kempner function (846 words) [view diff] exact match in snippet view article find links to article

{\displaystyle n} whose prime factorization is already known, by applying it separately to each prime power in the factorization and choosing the one that

Jens Franke (156 words) [view diff] exact match in snippet view article find links to article

In May 2007, he and his colleague Thorsten Kleinjung announced the factorization of M1039, the 1,039th Mersenne number. "Archived copy". Archived from

Newton's method in optimization (1,857 words) [view diff] exact match in snippet view article find links to article

applicable to certain types of equations, for example the Cholesky factorization and conjugate gradient will only work if f ″ ( x k ) {\displaystyle

Davison Soper (430 words) [view diff] exact match in snippet view article find links to article

parton model. With George Sterman and John C. Collins, he proved a factorization theorem in perturbative quantum chromodynamics (QCD). Soper is a member

Minimum degree algorithm (781 words) [view diff] exact match in snippet view article find links to article

later derived a graph theoretic version of the algorithm where the factorization is only simulated, and this was named the minimum degree algorithm.

Landau–Ramanujan constant (427 words) [view diff] exact match in snippet view article find links to article

even exponent in their prime factorization. For instance, 45 = 9 + 36 is a sum of two squares; in its prime factorization, 32 × 5, the prime 3 appears

Twinkle (322 words) [view diff] exact match in snippet view article find links to article

Qt-based VoIP soft phone for Linux TWINKLE, a hypothetical integer factorization device Twinkle (protein), a protein coded by a gene also called TWNK

Sibe Mardešić (463 words) [view diff] exact match in snippet view article find links to article

topological spaces. He introduced the first factorization theorem in dimension theory, the Mardešić factorization theorem. With P. Papić he introduced the

Mathematical induction (6,914 words) [view diff] no match in snippet view article find links to article

Mathematical induction is a method for proving that a statement P ( n ) {\displaystyle P(n)} is true for every natural number n {\displaystyle n} , that

Henk van der Vorst (694 words) [view diff] exact match in snippet view article find links to article

preconditioner, incomplete twisted factorizations, and the incomplete factorization based on the so-called "vdv" ordering. He is the author of the book

Triangular decomposition (1,610 words) [view diff] exact match in snippet view article find links to article

justifies the terminology. The Characteristic Set Method is the first factorization-free algorithm, which was proposed for decomposing an algebraic variety

Hessenberg matrix (1,958 words) [view diff] exact match in snippet view article find links to article

QR-factorization. In eigenvalue algorithms, the Hessenberg matrix can be further reduced to a triangular matrix through Shifted QR-factorization combined

Commutator collecting process (470 words) [view diff] exact match in snippet view article find links to article

the commutator collecting process. Hall words also provide a unique factorization of monoids. The commutator collecting process is usually stated for

Hans Riesel (597 words) [view diff] exact match in snippet view article find links to article

discrete logarithms. His monograph Prime Numbers and Computer Methods for Factorization (Birkhäuser, 1985; 2nd ed. 1994) synthesised that course and became

Triangular decomposition (1,610 words) [view diff] exact match in snippet view article find links to article

justifies the terminology. The Characteristic Set Method is the first factorization-free algorithm, which was proposed for decomposing an algebraic variety

Proof of Fermat's Last Theorem for specific exponents (5,155 words) [view diff] exact match in snippet view article find links to article

This unique factorization property is the basis on which much of number theory is built. One consequence of this unique factorization property is that

Linearised polynomial (1,068 words) [view diff] exact match in snippet view article find links to article

Fq of degree > 1 has a symbolic factorization into symbolically irreducible polynomials over Fq and this factorization is essentially unique (up to rearranging

53 equal temperament (2,922 words) [view diff] exact match in snippet view article find links to article

both 5 limit intervals, involving only the primes 2, 3, and 5 in their factorization, and the fact that 53 TET tempers out both characterizes it completely

Conductor (ring theory) (1,380 words) [view diff] exact match in snippet view article

interpretation of the conductor is that it measures the failure of unique factorization into prime ideals. Let A and B be commutative rings, and assume A ⊆

Gigla Janashia (858 words) [view diff] exact match in snippet view article find links to article

mathematician. He was the key author of Janashia-Lagvilava matrix spectral factorization (MSF) method. The major recognition of his achievements came after Janashia’s

Singly and doubly even (1,800 words) [view diff] exact match in snippet view article find links to article

an integer. This is equivalent to the multiplicity of 2 in the prime factorization. A singly even number can be divided by 2 only once; it is even but

Double Mersenne number (1,021 words) [view diff] exact match in snippet view article find links to article

factor of MM61 Archived 2009-02-08 at the Wayback Machine. Status of the factorization of double Mersenne numbers Double Mersennes Prime Search Operazione

ELSV formula (2,468 words) [view diff] exact match in snippet view article find links to article

{\displaystyle (\tau _{1},\dots ,\tau _{m},\sigma )} is a transitive factorization of identity of type (k1, ..., kn) if the product τ 1 ⋯ τ m σ {\displaystyle

Dryden Wind Turbulence Model (1,330 words) [view diff] exact match in snippet view article find links to article

of a minimum phase linear filter through a process known as spectral factorization. Consider a linear time invariant system with a white noise input that

Newton polygon (2,413 words) [view diff] exact match in snippet view article find links to article

{\displaystyle f} , a contradiction. More generally, the following factorization theorem holds: Assume that ( K , v K ) {\displaystyle (K,v_{K})} is

Symbolic Cholesky decomposition (310 words) [view diff] exact match in snippet view article find links to article

{\displaystyle A=LL^{T}\,} . In order to implement an efficient sparse factorization it has been found to be necessary to determine the non zero structure

Hamming space (579 words) [view diff] exact match in snippet view article find links to article

distinguish them from variable-length codes that are defined by unique factorization on a monoid. The Hamming distance endows a Hamming space with a metric

Von Kármán wind turbulence model (1,652 words) [view diff] exact match in snippet view article find links to article

of a minimum phase linear filter through a process known as spectral factorization. Consider a linear time invariant system with a white noise input that

Teiji Takagi (580 words) [view diff] exact match in snippet view article find links to article

development of Japanese encryption systems; see Purple. The Autonne-Takagi factorization of complex symmetric matrices is named in his honour. Sigekatu Kuroda

Congruence (339 words) [view diff] exact match in snippet view article find links to article

of squares, in number theory, a congruence commonly used in integer factorization algorithms Matrix congruence, an equivalence relation between two matrices

Tensor software (2,065 words) [view diff] exact match in snippet view article find links to article

an open source software package for high-performance sparse tensor factorization. SPLATT ships a stand-alone executable, C/C++ library, and Octave/MATLAB

Jim Coykendall (455 words) [view diff] exact match in snippet view article find links to article

particularly in the study of factorization properties of rings and ideals. He presented his work on Normsets and Factorization Properties of Rings of Integers

ML.NET (1,606 words) [view diff] exact match in snippet view article find links to article

in ML.NET. The release included other notable enhancements such as Factorization Machines, LightGBM, Ensembles, LightLDA transform and OVA. The ML.NET

Butcher group (4,050 words) [view diff] exact match in snippet view article find links to article

in quantum field theory. Renormalization was interpreted as Birkhoff factorization of loops in the character group of the associated Hopf algebra. The

Decomposition (disambiguation) (409 words) [view diff] exact match in snippet view article

Matrix decomposition, a factorization of a matrix into a product of matrices LU decomposition, a type of matrix factorization Permutation decomposition

Real-root isolation (4,602 words) [view diff] exact match in snippet view article find links to article

reasons for that. Firstly Yun's algorithm for computing the square-free factorization is less costly than twice the cost of the computation of the greatest

William B. Gragg (322 words) [view diff] exact match in snippet view article find links to article

the QR algorithm for unitary Hessenberg matrices, on updating the QR factorization, superfast solution of Toeplitz systems, parallel algorithms for solving

Nagata's compactification theorem (454 words) [view diff] exact match in snippet view article find links to article

{\displaystyle f:X\to S,} one defines R f ! {\displaystyle Rf_{!}} by choosing a factorization f = p ∘ j {\displaystyle f=p\circ j} by an open immersion j and proper

Ordered Bell number (5,086 words) [view diff] exact match in snippet view article find links to article

distinct prime numbers; 30 is squarefree, but 20 is not, because its prime factorization 2 · 2 · 5 repeats the prime 2. For squarefree numbers with n {\displaystyle

Perturbative quantum chromodynamics (1,005 words) [view diff] exact match in snippet view article find links to article

non-perturbative nature. To account for this, physicists[who?] developed the QCD factorization theorem, which separates the cross section into two parts: the process

Ladder height process (115 words) [view diff] exact match in snippet view article find links to article

process has achieved up to the specified point in time. The Wiener-Hopf factorization gives the transition probability kernel in the discrete time case. Record

Two-way string-matching algorithm (1,231 words) [view diff] exact match in snippet view article find links to article

partial repeats: the search pattern is split into two parts (its critical factorization), represented only by the position of that split. Being a number less

Hierarchical matrix (2,149 words) [view diff] exact match in snippet view article find links to article

results of matrix arithmetic operations like matrix multiplication, factorization or inversion can be approximated in O ( n k α log ⁡ ( n ) β ) {\displaystyle

Gravity R&D (936 words) [view diff] exact match in snippet view article find links to article

Pilászy; Dávid Zibriczky; Domonkos Tikk (2010), "Fast ALS-based matrix factorization for explicit and implicit feedback datasets", Proceedings of the fourth

SPIKE algorithm (3,549 words) [view diff] exact match in snippet view article find links to article

at m). Thus, a similar factorization step can be performed on S̃2 to produce S̃2 = D̃2S̃3 and S̃ = D̃1D̃2S̃3. Such factorization steps can be performed