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searching for Polynomial 73 found (5846 total)

alternate case: polynomial

Inequality (mathematics) (3,343 words) [view diff] exact match in snippet view article

decomposition is an algorithm that allows testing whether a system of polynomial equations and inequalities has solutions, and, if solutions exist, describing

Betti number (2,508 words) [view diff] exact match in snippet view article find links to article

generated homology, the Poincaré polynomial is defined as the generating function of its Betti numbers, via the polynomial where the coefficient of x n {\displaystyle

Weir (2,351 words) [view diff] exact match in snippet view article find links to article

A polynomial weir is a weir that has a geometry defined by a polynomial equation of any order n. In practice, most weirs are low-order polynomial weirs

Extrapolation (1,701 words) [view diff] exact match in snippet view article find links to article

series that fits the data. The resulting polynomial may be used to extrapolate the data. High-order polynomial extrapolation must be used with due care

Piecewise function (1,091 words) [view diff] exact match in snippet view article find links to article

function composed of power-law sub-functions Spline, a function composed of polynomial sub-functions, often constrained to be smooth at the joints between pieces

Commitment scheme (7,701 words) [view diff] exact match in snippet view article find links to article

reformulates the vector of values to be committed as a polynomial. First, we calculate a polynomial such that p ( i ) = x i {\displaystyle p(i)=x_{i}} for

Linear programming (6,690 words) [view diff] exact match in snippet view article find links to article

polynomial-time algorithm? Does LP admit a strongly polynomial-time algorithm to find a strictly complementary solution? Does LP admit a polynomial-time

Ulam spiral (2,572 words) [view diff] exact match in snippet view article find links to article

spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x2 − x + 41, are believed to produce

Parameterized complexity (2,684 words) [view diff] exact match in snippet view article find links to article

super-polynomial running time when complexity is measured in terms of the input size only but that are computable in a time that is polynomial in the

Divine Proportions: Rational Trigonometry to Universal Geometry (1,430 words) [view diff] no match in snippet view article find links to article

Divine Proportions: Rational Trigonometry to Universal Geometry is a 2005 book by the mathematician Norman J. Wildberger on a proposed alternative approach

Lucky numbers of Euler (326 words) [view diff] exact match in snippet view article find links to article

positive integers n such that for all integers k with 1 ≤ k < n, the polynomial k2 − k + n produces a prime number. When k is equal to n, the value cannot

Circuit complexity (2,571 words) [view diff] exact match in snippet view article find links to article

class P/poly consists of Boolean functions computable by circuits of polynomial size. Proving that N P ⊈ P / p o l y {\displaystyle {\mathsf {NP}}\not

Approximation error (2,701 words) [view diff] exact match in snippet view article find links to article

v is polynomially computable with relative error (utilizing an algorithm that we can designate as REL), then it is consequently also polynomially computable

Randomized algorithm (4,218 words) [view diff] exact match in snippet view article find links to article

computing the roots of a polynomial over a finite field. In 1977, Robert M. Solovay and Volker Strassen discovered a polynomial-time randomized primality

Autoregressive moving-average model (2,461 words) [view diff] exact match in snippet view article find links to article

process using autoregression (AR) and a moving average (MA), each with a polynomial. They are a tool for understanding a series and predicting future values

Donaldson theory (234 words) [view diff] no match in snippet view article find links to article

In mathematics, and especially gauge theory, Donaldson theory is the study of the topology of smooth 4-manifolds using moduli spaces of anti-self-dual

Computational problem (984 words) [view diff] exact match in snippet view article find links to article

classes P, problems that consume polynomial time for deterministic classical machines BPP, problems that consume polynomial time for probabilistic classical

Integer factorization (2,983 words) [view diff] exact match in snippet view article find links to article

Unsolved problem in computer science Can integer factorization be solved in polynomial time on a classical computer? More unsolved problems in computer science

Group method of data handling (2,585 words) [view diff] exact match in snippet view article find links to article

inductive procedure that performs sorting-out of gradually complicated polynomial models and selecting the best solution by means of the external criterion

Hilbert's sixteenth problem (1,243 words) [view diff] exact match in snippet view article find links to article

of the upper bound for the number of limit cycles in two-dimensional polynomial vector fields of degree n and an investigation of their relative positions

Cook–Levin theorem (2,354 words) [view diff] exact match in snippet view article find links to article

NP-complete. That is, it is in NP, and any problem in NP can be reduced in polynomial time by a deterministic Turing machine to the Boolean satisfiability problem

Hilbert's sixteenth problem (1,243 words) [view diff] exact match in snippet view article find links to article

of the upper bound for the number of limit cycles in two-dimensional polynomial vector fields of degree n and an investigation of their relative positions

Graph automorphism (1,343 words) [view diff] exact match in snippet view article find links to article

list of generators, is polynomial-time equivalent to the graph isomorphism problem, and therefore solvable in quasi-polynomial time, that is with running

Longest path problem (2,662 words) [view diff] exact match in snippet view article find links to article

edges. In contrast to the shortest path problem, which can be solved in polynomial time in graphs without negative-weight cycles, the longest path problem

Convex optimization (3,166 words) [view diff] exact match in snippet view article find links to article

over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard

Ring learning with errors signature (2,570 words) [view diff] exact match in snippet view article find links to article

2, the polynomial Φ(x) will be the cyclotomic polynomial xn + 1. Other choices of n are possible but the corresponding cyclotomic polynomials are more

Fulkerson Prize (1,965 words) [view diff] exact match in snippet view article find links to article

integer programs with few variables in time polynomial in the number of constraints. Eugene M. Luks for a polynomial time graph isomorphism algorithm for graphs

Primality test (3,833 words) [view diff] exact match in snippet view article find links to article

whereas primality testing is comparatively easy (its running time is polynomial in the size of the input). Some primality tests prove that a number is

Primality test (3,833 words) [view diff] exact match in snippet view article find links to article

whereas primality testing is comparatively easy (its running time is polynomial in the size of the input). Some primality tests prove that a number is

Fulkerson Prize (1,965 words) [view diff] exact match in snippet view article find links to article

integer programs with few variables in time polynomial in the number of constraints. Eugene M. Luks for a polynomial time graph isomorphism algorithm for graphs

Ring learning with errors signature (2,570 words) [view diff] exact match in snippet view article find links to article

2, the polynomial Φ(x) will be the cyclotomic polynomial xn + 1. Other choices of n are possible but the corresponding cyclotomic polynomials are more

Hp-FEM (1,912 words) [view diff] exact match in snippet view article find links to article

solving partial differential equations numerically based on piecewise-polynomial approximations. hp-FEM originates from the discovery by Barna A. Szabó

Probabilistic Turing machine (1,061 words) [view diff] exact match in snippet view article find links to article

the class of languages recognized by a probabilistic Turing machine in polynomial time with an error probability of 1/3. Another class defined using this

Lamé function (1,787 words) [view diff] exact match in snippet view article find links to article

some special cases solutions can be expressed in terms of polynomials called Lamé polynomials. Lamé's equation is d 2 y d x 2 + ( A + B ℘ ( x ) ) y = 0

Natural Earth projection (608 words) [view diff] exact match in snippet view article find links to article

the creation of new projections. Subsequently, Bojan Šavrič developed a polynomial expression of the projection. The projection may also be referred to as

Genus of a multiplicative sequence (2,718 words) [view diff] exact match in snippet view article find links to article

numbers, having the property that they are constructed from a sequence of polynomials in characteristic classes that arise as coefficients in formal power

Control-flow analysis (264 words) [view diff] no match in snippet view article find links to article

In computer science, control-flow analysis (CFA) is a static-code-analysis technique for determining the control flow of a program. The control flow is

Change of variables (2,691 words) [view diff] exact match in snippet view article find links to article

the roots of the sixth-degree polynomial: x 6 − 9 x 3 + 8 = 0. {\displaystyle x^{6}-9x^{3}+8=0.} Sixth-degree polynomial equations are generally impossible

Average-case complexity (2,834 words) [view diff] exact match in snippet view article find links to article

\{0,1\}^{n}:y\leq x}\Pr[y]} in polynomial time. This implies that Pr[x] is also computable in polynomial time. Polynomial-time samplable distributions (P-samplable):

Special linear group (1,781 words) [view diff] exact match in snippet view article find links to article

subvariety of the general linear group – they satisfy a polynomial equation (since the determinant is polynomial in the entries). When R {\displaystyle R} is the

Computer-automated design (1,355 words) [view diff] exact match in snippet view article find links to article

evolutionary algorithm (EA) can be used instead, which is a (non-deterministic) polynomial algorithm. The EA based multi-objective "search team" can be interfaced

Karmarkar's algorithm (2,243 words) [view diff] exact match in snippet view article find links to article

efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice.

Karmarkar's algorithm (2,243 words) [view diff] exact match in snippet view article find links to article

efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice.

Computational learning theory (865 words) [view diff] exact match in snippet view article find links to article

learning theory, a computation is considered feasible if it can be done in polynomial time.[citation needed] There are two kinds of time complexity results:

Arrangement of hyperplanes (1,806 words) [view diff] exact match in snippet view article find links to article

−1.) This polynomial helps to solve some basic questions; see below. Another polynomial associated with A is the Whitney-number polynomial wA(x, y), defined

Finite difference method (3,607 words) [view diff] exact match in snippet view article find links to article

the Taylor polynomial can be used to analyze local truncation error. Using the Lagrange form of the remainder from the Taylor polynomial for f ( x 0

Adleman–Pomerance–Rumely primality test (255 words) [view diff] no match in snippet view article find links to article

In computational number theory, the Adleman–Pomerance–Rumely primality test is an algorithm for determining whether a number is prime. Unlike other, more

Ellipsoid method (3,704 words) [view diff] exact match in snippet view article find links to article

algorithm which finds an optimal solution in a number of steps that is polynomial in the input size. The ellipsoid method has a long history. As an iterative

Hamiltonian path (2,043 words) [view diff] exact match in snippet view article find links to article

assigned weights from a certain ground field) is the Hamiltonian cycle polynomial of its weighted adjacency matrix defined as the sum of the products of

Dirichlet series (5,355 words) [view diff] no match in snippet view article find links to article

In mathematics, a Dirichlet series is any series of the form ∑ n = 1 ∞ a n n s , {\displaystyle \sum _{n=1}^{\infty }{\frac {a_{n}}{n^{s}}},} where s is

G2 (mathematics) (2,056 words) [view diff] exact match in snippet view article

called G2-manifolds. G2 is the automorphism group of the following two polynomials in 7 non-commutative variables. C 1 = t 2 + u 2 + v 2 + w 2 + x 2 + y

Philosophy of computer science (909 words) [view diff] exact match in snippet view article find links to article

solution can be verified in polynomial time (and so defined to belong to the class NP) can also be solved in polynomial time (and so defined to belong

Merkle–Hellman knapsack cryptosystem (1,852 words) [view diff] exact match in snippet view article find links to article

cryptosystems. It was published by Ralph Merkle and Martin Hellman in 1978. A polynomial time attack was published by Adi Shamir in 1984. As a result, the cryptosystem

Computational indistinguishability (420 words) [view diff] exact match in snippet view article find links to article

computationally indistinguishable if for any non-uniform probabilistic polynomial time algorithm A, the following quantity is a negligible function in n:

Concatenated error correction code (2,088 words) [view diff] exact match in snippet view article find links to article

exponentially decreasing error probability with increasing block length and polynomial-time decoding complexity. Concatenated codes became widely used in space

Graph minor (4,046 words) [view diff] exact match in snippet view article find links to article

H, it is possible to test whether H is a minor of an input graph G in polynomial time; together with the forbidden minor characterization this implies

Non-standard positional numeral systems (1,389 words) [view diff] exact match in snippet view article find links to article

number. The value of a digit string like pqrs in base b is given by the polynomial form p × b 3 + q × b 2 + r × b + s {\displaystyle p\times b^{3}+q\times

Theodore Motzkin (661 words) [view diff] exact match in snippet view article find links to article

first explicit example of a nonnegative polynomial which is not a sum of squares, known as the Motzkin polynomial X 4 Y 2 + X 2 Y 4 − 3 X 2 Y 2 + 1 {\displaystyle

E7 (mathematics) (2,831 words) [view diff] exact match in snippet view article

to the right. E7 is the automorphism group of the following pair of polynomials in 56 non-commutative variables. We divide the variables into two groups

Interior-point method (4,691 words) [view diff] exact match in snippet view article find links to article

advantages of previously-known algorithms: Theoretically, their run-time is polynomial—in contrast to the simplex method, which has exponential run-time in the

Proof complexity (3,754 words) [view diff] exact match in snippet view article find links to article

polynomial-size proofs of all tautologies. Here the size of the proof is simply the number of symbols in it, and a proof is said to be of polynomial size

Semialgebraic set (429 words) [view diff] exact match in snippet view article find links to article

mathematics, a basic semialgebraic set is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraic set is a finite union of

Maximum cut (3,125 words) [view diff] exact match in snippet view article find links to article

inspection problem may be solved in polynomial time, and this duality allows the maximum cut problem to also be solved in polynomial time for planar graphs. The

Johannes Hudde (542 words) [view diff] exact match in snippet view article find links to article

necessary to determine a double root to a polynomial equation. And establishing two properties of polynomial roots known as Hudde's rules, that point toward

Systolic array (2,147 words) [view diff] exact match in snippet view article find links to article

applications include computing greatest common divisors of integers and polynomials. They are sometimes classified as multiple-instruction single-data (MISD)

Systolic array (2,147 words) [view diff] exact match in snippet view article find links to article

applications include computing greatest common divisors of integers and polynomials. They are sometimes classified as multiple-instruction single-data (MISD)

Johannes Hudde (542 words) [view diff] exact match in snippet view article find links to article

necessary to determine a double root to a polynomial equation. And establishing two properties of polynomial roots known as Hudde's rules, that point toward

Infinite element method (212 words) [view diff] exact match in snippet view article find links to article

infinite length. In contrast with a finite element which is approximated by polynomial expressions on a finite support, the unbounded length of the infinite

Bicomplex number (1,806 words) [view diff] exact match in snippet view article find links to article

tessarines T is isomorphic to 2C, the rings of polynomials T[X] and 2C[X] are also isomorphic, however polynomials in the latter algebra split: ∑ k = 1 n (

Cryptographically secure pseudorandom number generator (3,633 words) [view diff] exact match in snippet view article find links to article

test. That is, given the first k bits of a random sequence, there is no polynomial-time algorithm that can predict the (k+1)th bit with probability of success

Transcendence (500 words) [view diff] exact match in snippet view article find links to article

refer to: Transcendental number, a number that is not the root of any polynomial with rational coefficients Algebraic element or transcendental element

Frobenius method (2,955 words) [view diff] exact match in snippet view article find links to article

is known as the indicial polynomial, which is quadratic in r. The general definition of the indicial polynomial is the coefficient of the lowest

Toom–Cook multiplication (3,101 words) [view diff] exact match in snippet view article find links to article

The Toom–Cook approach to computing the polynomial product p(x)q(x) is a commonly used one. Note that a polynomial of degree d is uniquely determined by