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searching for System of linear equations 84 found (227 total)

alternate case: system of linear equations

Basis pursuit (482 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

Indeterminate system (582 words) [view diff] exact match in snippet view article find links to article

consistent, in the sense of having at least one solution. For a system of linear equations, the number of equations in an indeterminate system could be the

Llewellyn Thomas (905 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) (582 words) [view diff] exact match in snippet view article

Kombinatorik. Let Ax=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 (2,169 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 (502 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 Ax=b{\displaystyle Ax=b}, where: A{\displaystyle A} is a sparse

Finite-difference frequency-domain method (931 words) [view diff] exact match in snippet view article find links to article

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

Wilson matrix (1,132 words) [view diff] exact match in snippet view article find links to article

This is the coefficient matrix of the following system of linear equations considered in a paper by J. Morris published in 1946: (S1) 5 x

Guyan reduction (684 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) (682 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: [K11K12K21K22][x1x2]=[F1F2]{\displaystyle

Geopositioning (999 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

Retrieval Data Structure (1,502 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

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)

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

Validated numerics (1,339 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) (555 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 a11x1+⋯+a1nxn=a1,n+1xn+1⋮an−k,1x1+⋯+an−k,nxn=an−k,n+1xn+1

Linear least squares (5,055 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

Farkas' lemma (2,828 words) [view diff] exact match in snippet view article find links to article

: 92–94 Farkas' lemma implies that the decision problem "Given a system of linear equations, does it have a non-negative solution?" is in the intersection

Newton polynomial (5,262 words) [view diff] exact match in snippet view article find links to article

leads to a problem in linear algebra where we have to solve a system of linear equations. Using a standard monomial basis for our interpolation polynomial

Prony's method (1,096 words) [view diff] exact match in snippet view article find links to article

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

Ordinary least squares (8,490 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

MAX-3SAT (1,433 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

Rand McNally (2,914 words) [view diff] exact match in snippet view article find links to article

random variable. Gaussian elimination method is used to solve a system of linear equations. In the 1950's this was the work of many mathematicians that put

Taxicab geometry (2,403 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 (692 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 (970 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

Coefficients of potential (969 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 ϕ1=p11Q1+p12Q2ϕ2=p21Q1+p22Q2.{\displaystyle {\begin{matrix}\phi

Input–output model (2,927 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)−1d=[19.1912.97].{\displaystyle

Triangular matrix (2,943 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 ℓ1,1x1=b1ℓ2,1x1+ℓ2,2x2=b2⋮⋮⋱⋮ℓm,1x1+ℓm,2x2+⋯+ℓm,mxm=bm{\displaystyle

Incidence (geometry) (1,618 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

A5/1 (2,676 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

Möller–Trumbore intersection algorithm (1,506 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

The Nine Chapters on the Mathematical Art (2,471 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

Orthogonal matrix (4,548 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

Mediant (mathematics) (1,869 words) [view diff] exact match in snippet view article

λ2{\displaystyle \lambda _{1},\,\lambda _{2}} must be integers, solving the system of linear equations a′=λ1a+λ2b{\displaystyle a'=\lambda _{1}a+\lambda _{2}b}

Equivalent impedance transforms (3,444 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):

Volterra integral equation (1,366 words) [view diff] exact match in snippet view article find links to article

Kij=K(ti,sj){\displaystyle K_{ij}=K(t_{i},s_{j})}, we have the system of linear equations: x0=f0x1=f1+Δs2(K10x0+K11x1)x2=f2+Δs2(K20x0+2K21x1+K22x2)⋮xn=

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

Gradient descent (5,015 words) [view diff] exact match in snippet view article find links to article

the global solution. Gradient descent can be used to solve a system of linear equations Ax−b=0{\displaystyle A\mathbf {x} -\mathbf {b} =0} reformulated

Maximum cut (2,747 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

Aerodynamic potential-flow code (1,436 words) [view diff] exact match in snippet view article find links to article

mi={\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

Ellipsoid method (3,570 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

Linear differential equation (4,446 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 (2,616 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 [ABCD][xy]=[uv]{\displaystyle {\begin{bmatrix}A&B\\C&

Fangcheng (mathematics) (1,084 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

Unique games conjecture (2,586 words) [view diff] exact match in snippet view article find links to article

terms of linear equations. For example, suppose that we have a system of linear equations over the integers modulo 7: x1≡2⋅x2(mod7),x2≡4⋅x5(mod7), ⋮x1≡2⋅x7(mod7)

Thermal simulations for integrated circuits (1,944 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

Elastic collision (4,599 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 v1,v2,{\displaystyle v_{1},v_{2},} regarding m1,m2,u1,u2{\displaystyle

Reed–Solomon error correction (11,096 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.

Discrete dipole approximation (2,552 words) [view diff] exact match in snippet view article find links to article

rectangular cuboid), conjugate gradient method to solve large system of linear equations, and FFT-acceleration of the matrix-vector products which uses

Mehrotra predictor–corrector method (1,501 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)[ΔxaffΔλaffΔsaff]=−F(x,λ,s){\displaystyle J(x,\lambda

Boolean satisfiability problem (5,312 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;

Matrix differential equation (2,514 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=2A+B{\displaystyle 1=2A+B} 1=A+2B .{\displaystyle 1=A+2B~.}

Trigonometry of a tetrahedron (2,383 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: {−Δ1+Δ2c34+Δ3c24+Δ4c23=0Δ1c34−Δ2+Δ3c14+Δ4c13=0Δ1c24+Δ2c14−Δ3

Stochastic dominance (3,511 words) [view diff] exact match in snippet view article find links to article

used, 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

Computational fluid dynamics (8,481 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

Info-metrics (2,031 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

Robert J. Marks II (3,570 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

Sensor array (2,722 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

Global Positioning System (18,385 words) [view diff] case mismatch in snippet view article find links to article

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

Sensor array (2,722 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 (11,971 words) [view diff] exact match in snippet view article find links to article

γμ{\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

History of computed tomography (2,555 words) [view diff] exact match in snippet view article find links to article

Mathématiques. 35: 355–7. Kaczmarz S., "Approximate solution of system of linear equations. Int. J. Control. 1993; 57-9. Cormack AM (1963). "Representation

Causal model (6,005 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

List of eponymous laws (10,123 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

Carl Friedrich Gauss (19,321 words) [view diff] exact match in snippet view article find links to article

to Gerling from 1823, he described a solution of a certain 4X4 system of linear equations by using Gauss-Seidel method – an "indirect" iterative method

Steinitz's theorem (5,924 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

Mathematical economics (13,530 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

Gottfried Wilhelm Leibniz (18,753 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

Eldon Hansen (1,938 words) [view diff] exact match in snippet view article find links to article

Hansen, Eldon; Smith, Roberta. A computer program for solving a system of linear equations and matrix inversion with automatic error bounding using interval

Medical image computing (8,460 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 (9,016 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 (ATA)−1AT{\displaystyle (A^{T}A)^{-1}A^{T}}

Hückel method (6,720 words) [view diff] exact match in snippet view article find links to article

…,cn){\displaystyle (c_{1},c_{2},\ldots ,c_{n})} to the above system of linear equations can only exist if the coefficient matrix [Hij−ESij]{\displaystyle

History of algebra (16,625 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

List of important publications in mathematics (10,114 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

Interval finite element (6,031 words) [view diff] exact match in snippet view article find links to article

Popova and Skalna introduced the methods for the solution of the system of linear equations in which the coefficients are linear combinations of interval

Flux balance analysis (5,739 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

Transfer length method (4,551 words) [view diff] exact match in snippet view article find links to article

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

List of Chinese inventions (34,922 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

Geometric rigidity (5,337 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))=0,{\displaystyle (p(u)-p(v))\cdot

Flow cytometry bioinformatics (8,058 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 (5,562 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 (10,044 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