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searching for System of linear equations 77 found (226 total)

alternate case: system of linear equations

Basis pursuit (559 words) [view diff] exact match in snippet view article find links to article

is usually applied in cases where there is an underdetermined system of linear equations y = Ax that must be exactly satisfied, and the sparsest solution

Llewellyn Thomas (888 words) [view diff] exact match in snippet view article find links to article

theory), and devising an efficient method for solving tridiagonal system of linear equations (Thomas algorithm). Born in London, he studied at Cambridge University

MAX-3LIN-EQN (110 words) [view diff] exact match in snippet view article find links to article

problem in Computational complexity theory where the input is a system of linear equations (modulo 2). Each equation contains at most 3 variables. The problem

Rado's theorem (Ramsey theory) (606 words) [view diff] exact match in snippet view article

Let A x = 0 {\displaystyle A\mathbf {x} =\mathbf {0} } be a system of linear equations, where A {\displaystyle A} is a matrix with integer entries. This

Random walker algorithm (2,256 words) [view diff] exact match in snippet view article find links to article

These probabilities may be determined analytically by solving a system of linear equations. After computing these probabilities for each pixel, the pixel

Algebraic reconstruction technique (521 words) [view diff] exact match in snippet view article find links to article

reconstruction process. ART can be considered as an iterative solver of a system of linear equations A x = b {\displaystyle Ax=b} , where: A {\displaystyle A} is a

Finite-difference frequency-domain method (938 words) [view diff] exact match in snippet view article find links to article

frequency-domain response problem leads to an A x = b {\displaystyle Ax=b} system of linear equations as described above. An early description of a frequency-domain

Guyan reduction (861 words) [view diff] exact match in snippet view article find links to article

length of the displacement vector. By partitioning the above system of linear equations with regards to loaded (master) and unloaded (slave) degrees of

Reduction (mathematics) (725 words) [view diff] exact match in snippet view article

is prone to some error in the solution. Consider the following system of linear equations in an FEA problem: [ K 11 K 12 K 21 K 22 ] [ x 1 x 2 ] = [ F 1

Retrieval Data Structure (1,514 words) [view diff] exact match in snippet view article find links to article

{\displaystyle (h(x))_{x\in S}} are linearly independent the following system of linear equations has a solution Z ∈ { 0 , 1 } m × r {\displaystyle Z\in \{0,1\}^{m\times

Gosper's algorithm (582 words) [view diff] exact match in snippet view article find links to article

finding that there is no such ƒ) is then a matter of solving a system of linear equations. Gosper's algorithm can be used to discover Wilf–Zeilberger pairs

Geopositioning (1,211 words) [view diff] exact match in snippet view article find links to article

observations to compute a position fix is equivalent to solving a system of linear equations. Navigation systems use regression algorithms such as least squares

Additive Schwarz method (1,251 words) [view diff] exact match in snippet view article find links to article

usually not possible to split our grid of 64 points (a 64×64 system of linear equations) into two grids of 32 points (two 32×32 systems of linear equations)

Validated numerics (1,341 words) [view diff] exact match in snippet view article find links to article

numerical linear algebra Validating numerical solutions of a given system of linear equations Validating numerically obtained eigenvalues Rigorously computing

Affine Grassmannian (manifold) (599 words) [view diff] exact match in snippet view article

n}x_{n}&=a_{n-k,n+1}.\end{aligned}}} These determine a rank n−k system of linear equations on Rn+1 a 11 x 1 + ⋯ + a 1 n x n = a 1 , n + 1 x n + 1 ⋮ a n −

Linear least squares (5,375 words) [view diff] exact match in snippet view article find links to article

squares is the problem of approximately solving an overdetermined system of linear equations A x = b, where b is not an element of the column space of the

Scientific programming language (756 words) [view diff] exact match in snippet view article find links to article

mathematical constructs. For example, the following Julia code solves a system of linear equations: A = rand(20, 20) # A is a 20x20 matrix b = rand(20) # b is a

MAX-3SAT (1,450 words) [view diff] exact match in snippet view article find links to article

equated to "=1" as usual, one could find a proof π by solving a system of linear equations (see MAX-3LIN-EQN) implying P = NP. If z ∈ L, a fraction ≥ (1

Prony's method (1,285 words) [view diff] exact match in snippet view article find links to article

_{m}}} values, the F n {\displaystyle F_{n}} values are part of a system of linear equations that may be used to solve for the B m {\displaystyle \mathrm {B}

Ordinary least squares (9,127 words) [view diff] exact match in snippet view article find links to article

mathematicians, OLS is an approximate solution to an overdetermined system of linear equations Xβ ≈ y, where β is the unknown. Assuming the system cannot be

Triangular matrix (3,152 words) [view diff] exact match in snippet view article find links to article

inverting the matrix. The matrix equation Lx = b can be written as a system of linear equations ℓ 1 , 1 x 1 = b 1 ℓ 2 , 1 x 1 + ℓ 2 , 2 x 2 = b 2 ⋮ ⋮ ⋱ ⋮ ℓ m

A5/1 (2,725 words) [view diff] exact match in snippet view article find links to article

of 240.16 (the units are in terms of number of solutions of a system of linear equations which are required). In 2000, Alex Biryukov, Adi Shamir and David

Leslie Fox (1,228 words) [view diff] exact match in snippet view article find links to article

by finite difference method and thus reducing the problem to a system of linear equations was the same. Careful analysis of the errors was a theme of many

The Nine Chapters on the Mathematical Art (2,338 words) [view diff] exact match in snippet view article find links to article

unknowns, and the most complex example analyzes the solution to a system of linear equations with up to 5 unknowns. The word jiu, or "9", means more than just

Taxicab geometry (2,507 words) [view diff] exact match in snippet view article find links to article

orientation in taxicab geometry. In solving an underdetermined system of linear equations, the regularization term for the parameter vector is expressed

Gebhart factor (762 words) [view diff] exact match in snippet view article find links to article

_{j=1}^{N_{s}}(B_{ij})=1} Several approaches exists to describe this as a system of linear equations that can be solved by Gaussian elimination or similar methods

Beam and Warming scheme (1,063 words) [view diff] exact match in snippet view article find links to article

n}-A_{i-1}^{n}u_{i-1}^{n}\right)\end{aligned}}} This resulted system of linear equations can be solved using the modified tridiagonal matrix algorithm

Optical flow (3,109 words) [view diff] exact match in snippet view article find links to article

discrete pixels, these equations are discretised. Doing so yields a system of linear equations which can be solved for ( u , v ) {\displaystyle (u,v)} at each

Möller–Trumbore intersection algorithm (1,585 words) [view diff] exact match in snippet view article find links to article

}&=-tD+u(v_{2}-v_{1})+v(v_{3}-v_{1})\end{aligned}}} This is a system of linear equations with three equations (one each for x {\displaystyle x} , y {\displaystyle

Incidence (geometry) (1,733 words) [view diff] exact match in snippet view article

that is the simultaneous solution (up to a scalar factor) of the system of linear equations: a1x + b1y + c1z = 0 and a2x + b2y + c2z = 0. The solution of

Coefficients of potential (1,191 words) [view diff] exact match in snippet view article find links to article

capacitance on a two-conductor system. For a two-conductor system, the system of linear equations is ϕ 1 = p 11 Q 1 + p 12 Q 2 ϕ 2 = p 21 Q 1 + p 22 Q 2 . {\displaystyle

Equivalent impedance transforms (3,538 words) [view diff] exact match in snippet view article find links to article

The entries of the matrix are chosen so that the matrix forms a system of linear equations in the mesh voltages and currents (as defined for mesh analysis):

Input–output model (4,061 words) [view diff] exact match in snippet view article find links to article

want 7 units of good A and 4 units of good B. Then solving the system of linear equations derived above gives us x = ( I − A ) − 1 y = [ 19.19 12.97 ]

Volterra integral equation (1,496 words) [view diff] exact match in snippet view article find links to article

i , s j ) {\displaystyle K_{ij}=K(t_{i},s_{j})} , we have the system of linear equations: x 0 = f 0 x 1 = f 1 + Δ s 2 ( K 10 x 0 + K 11 x 1 ) x 2 = f 2

Orthogonal matrix (4,802 words) [view diff] exact match in snippet view article find links to article

S symmetric positive-semidefinite Consider an overdetermined system of linear equations, as might occur with repeated measurements of a physical phenomenon

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

constraints, which can be solved by any method for solving a system of linear equations. Step 3: the decision problem can be reduced to a different optimization

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

Thomassé, S.; Yeo, A. (2014), "Satisfying more than half of a system of linear equations over GF(2): A multivariate approach", J. Comput. Syst. Sci., 80

Linear differential equation (4,754 words) [view diff] exact match in snippet view article find links to article

are partial derivatives. A linear differential equation or a system of linear equations such that the associated homogeneous equations have constant coefficients

Schur complement (2,901 words) [view diff] exact match in snippet view article find links to article

Laplacian matrix. The Schur complement arises naturally in solving a system of linear equations such as [ A B C D ] [ x y ] = [ u v ] {\displaystyle

Thermal simulations for integrated circuits (2,063 words) [view diff] exact match in snippet view article find links to article

Finally, a direct or iterative method is employed to solve the system of linear equations. For the thermal case, FEM method is more suitable due to the

Aerodynamic potential-flow code (1,541 words) [view diff] exact match in snippet view article find links to article

= {\displaystyle m_{i}=} These terms can be used to create a system of linear equations which can be solved for all the unknown values of λ {\displaystyle

Reed–Solomon error correction (12,395 words) [view diff] exact match in snippet view article find links to article

locations. There is a linear recurrence relation that gives rise to a system of linear equations. Solving those equations identifies those error locations Xk.

Unique games conjecture (3,066 words) [view diff] exact match in snippet view article find links to article

constraints over alphabet of size k is NP-hard. Consider the following system of linear equations over the integers modulo k: a 1 x 1 ≡ b 1 ⋅ x 2 + c 1 ( mod k

Mediant (mathematics) (2,038 words) [view diff] exact match in snippet view article

{\displaystyle \lambda _{1},\,\lambda _{2}} must be integers, solving the system of linear equations a ′ = λ 1 a + λ 2 b {\displaystyle a'=\lambda _{1}a+\lambda _{2}b}

Boolean satisfiability problem (5,112 words) [view diff] exact match in snippet view article find links to article

This is in P, since an XOR-SAT formula can also be viewed as a system of linear equations mod 2, and can be solved in cubic time by Gaussian elimination;

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

scaling direction. This is achieved by solving the following system of linear equations J ( x , λ , s ) [ Δ x aff Δ λ aff Δ s aff ] = − F ( x , λ , s

Fangcheng (mathematics) (1,198 words) [view diff] exact match in snippet view article

a unique solution. This is the earliest known reference to a system of linear equations in which the number of unknowns exceeds the number of equations

Info-metrics (2,101 words) [view diff] exact match in snippet view article find links to article

and James Mammen. "The simplest solution to an underdetermined system of linear equations". In Information Theory, 2006 IEEE International Symposium on

Computational fluid dynamics (8,648 words) [view diff] exact match in snippet view article find links to article

algebraic equations. Applying a Newton or Picard iteration produces a system of linear equations which is nonsymmetric in the presence of advection and indefinite

Matrix differential equation (2,732 words) [view diff] exact match in snippet view article find links to article

above equations equal 1. Thus we may construct the following system of linear equations, 1 = 2 A + B {\displaystyle 1=2A+B} 1 = A + 2 B . {\displaystyle

Robert J. Marks II (3,574 words) [view diff] exact match in snippet view article find links to article

of them can be obtained from the remaining ones by solving a system of linear equations". Ill-posed sampling (The Cheung-Marks Theorem). The sampling

Elastic collision (5,826 words) [view diff] exact match in snippet view article find links to article

by the collision. Now the above formulas follow from solving a system of linear equations for v A 2 , v B 2 , {\displaystyle v_{A2},v_{B2},} regarding m

Laplace transform (9,453 words) [view diff] exact match in snippet view article find links to article

convolution equations, the Laplace transform converts it into a system of linear equations for π n ( s ) = L ( P n ) ( s ) , {\displaystyle \pi _{n}(s)={\mathcal

Stochastic dominance (3,659 words) [view diff] exact match in snippet view article find links to article

u ( x ) {\displaystyle u(x)} is nondecreasing and concave. A system of linear equations can test whether a given solution if efficient for any such utility

Chinese mathematics (7,988 words) [view diff] exact match in snippet view article find links to article

or what is now known as linear algebra. Chapter seven solves system of linear equations with two unknowns using the false position method, similar to

Mathematical economics (10,736 words) [view diff] exact match in snippet view article find links to article

function with respect to quantity supplied for each firm left a system of linear equations, the simultaneous solution of which gave the equilibrium quantity

Global Positioning System (19,119 words) [view diff] case mismatch in snippet view article find links to article

1994. Oszczak, B., "New Algorithm for GNSS Positioning Using System of Linear Equations", Proceedings of the 26th International Technical Meeting of The

Sensor array (2,823 words) [view diff] exact match in snippet view article find links to article

its derivative (which is linear), let it equal zero and solve a system of linear equations. In ML beamformers the quadratic penalty function is used to the

Dirac equation (13,120 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \gamma ^{\mu }} , solving this is a matter of solving a system of linear equations. It is a representation-free property of gamma matrices that the

Carl Friedrich Gauss (17,929 words) [view diff] exact match in snippet view article find links to article

letter to Gerling from 1823, he described a solution of a 4x4 system of linear equations with the Gauss-Seidel method – an "indirect" iterative method

Trigonometry of a tetrahedron (3,048 words) [view diff] exact match in snippet view article find links to article

faces of the tetrahedron, one obtains the following homogeneous system of linear equations: { − Δ 1 + Δ 2 c 34 + Δ 3 c 24 + Δ 4 c 23 = 0 Δ 1 c 34 − Δ 2 +

Gottfried Wilhelm Leibniz (19,219 words) [view diff] exact match in snippet view article find links to article

if machines were used." Leibniz arranged the coefficients of a system of linear equations into an array, now called a matrix, in order to find a solution

List of eponymous laws (10,530 words) [view diff] exact match in snippet view article find links to article

In linear algebra, an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system

Causal model (6,184 words) [view diff] exact match in snippet view article find links to article

introduced principles for detecting and evaluating mediation in a system of linear equations. As of 2014 their paper was the 33rd most-cited of all time.: 324

Steinitz's theorem (5,973 words) [view diff] exact match in snippet view article find links to article

of a drawing of a graph. The method continues by setting up a system of linear equations in the vertex coordinates, according to which each remaining vertex

Medical image computing (8,475 words) [view diff] exact match in snippet view article find links to article

estimate of the diffusion tensor can be found by simply solving a system of linear equations at each location independently. However, as the volume is assumed

Scale-invariant feature transform (9,232 words) [view diff] exact match in snippet view article find links to article

A{\hat {\mathbf {x} }}=A^{T}\mathbf {b} .} The solution of the system of linear equations is given in terms of the matrix ( A T A ) − 1 A T {\displaystyle

History of algebra (17,047 words) [view diff] exact match in snippet view article find links to article

geometrical associations. Leibniz realized that the coefficients of a system of linear equations could be arranged into an array, now called a matrix, which can

Flux balance analysis (5,950 words) [view diff] exact match in snippet view article find links to article

reactions than metabolites and this gives an under-determined system of linear equations containing more variables than equations. The standard approach

Hückel method (7,290 words) [view diff] exact match in snippet view article find links to article

n ) {\displaystyle (c_{1},c_{2},\ldots ,c_{n})} to the above system of linear equations can only exist if the coefficient matrix [ H i j − E S i j ] {\displaystyle

List of publications in mathematics (10,420 words) [view diff] exact match in snippet view article find links to article

the earliest description of Gaussian elimination for solving system of linear equations, it also contains method for finding square root and cubic root

List of Chinese inventions (32,370 words) [view diff] exact match in snippet view article find links to article

towns and villages. Gaussian elimination: The Chinese solved a system of linear equations. The rectangle of coefficients was reduced to triangular and then

Transfer length method (5,102 words) [view diff] exact match in snippet view article find links to article

corresponding to a different gap length d i {\displaystyle d_{i}} - a system of linear equations can be obtained, which can be written in matrix-vector form. [

Geometric rigidity (5,449 words) [view diff] exact match in snippet view article find links to article

matrix. The Jacobian, or derivative, of the rigidity map yields a system of linear equations of the form ( p ( u ) − p ( v ) ) ⋅ ( p ′ ( v ) − p ′ ( u ) )

Flow cytometry bioinformatics (8,040 words) [view diff] exact match in snippet view article find links to article

signal to remove from each channel can be computed by solving a system of linear equations based on this data to produce a spillover matrix, which when inverted

Geiringer–Laman theorem (5,841 words) [view diff] exact match in snippet view article find links to article

an easier approach, because infinitesimal rigidity involves a system of linear equations, rather than quadratic in the case of regular rigidity. In particular

Pseudo-range multilateration (9,850 words) [view diff] exact match in snippet view article find links to article

non-linear equations (1, 2, 3). The TDOA problem can be turned into a system of linear equations when there are three or more receivers, which can reduce the computation