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Linear Equations

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Systems of linear equations

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Systems of linear equations Equivalent systems of linear equations Examples equivalent systems Row-transformations The Gauss method Example 1 Example 2 Example 3 Example 4 Equivalent systems of linear equations Examples / x+2y+3z=5 | x-y+6z=1 | 3x-2y=4 \ y+4z=8 / x+y+3z-4t=12 \ 3x+y-2z-t=0 / 2x+3y+4z=5 | x-y+2z=6 \ 3x-5y-z=0 Each of these systems can be expressed by the help of matrices. [ 1 2 3] [x] [5] [ 1 -1 6] . [y] = [1] [ 3 -2 0] [z] [4] [ 0 1 4] [8] [x] [ 1 1 3 -4] [y] [12] [ 3 1 -2 -1] . [z] = [ 0] [t] [ 2 3 4] [x] [5] [ 1 -1 2] . [y] = [6] [ 3 -5 -1] [z] [0] The first matrix of each representation of a linear system contains the coefficients appearing in the system. This matrix is called the coefficient matrix. The essential information of such system is this coefficient matrix A Read More
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Iterative Methods Library in C++

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IML++ (Iterative Methods Library) v. 1.2a IML++ is a C++ templated library of modern iterative methods for solving both symmetric and nonsymmetric linear systems of equations. The algorithms are fully templated in that the same source code works for dense, sparse, and distributed matrices. Some of the numerical methods are presented in the book, Templates: Building Blocks for the Solution of Iterative Systems and include Richardson Iteration Chebyshev Iteration Conjugate Gradient (CG) Conjugate Gradient Squared (CGS) BiConjugate Gradient (BiCG) BiConjugate Gradient Stabilized (BiCGSTAB) Generalized Minimum Residual (GMRES) Quasi-Minimal Residual Without Lookahead (QMR) The IML++ software also contains an optional test suite for sparse matrix computations, using SparseLib++ . IML++ Document Read More
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