gmres


gmres, a MATLAB code which applies the Generalized Minimum Residual (GMRES) method to solve a large, sparse system of linear equations.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

gmres is available in a MATLAB version and an Octave version.

Related Data and Programs:

gmres_test

bicg, a MATLAB code which implements the biconjugate gradient method (BICG), which estimates the solution of a large sparse nonsymmetric linear system.

cg, a MATLAB code which implements a simple version of the conjugate gradient (CG) method for solving a system of linear equations of the form A*x=b, suitable for situations where the matrix A is symmetric positive definite (SPD) (only real, positive eigenvalues).

cg_rc, a MATLAB code which implements the conjugate gradient method for solving a positive definite sparse linear system A*x=b, using reverse communication.

cg_squared, a MATLAB code which implements the conjugate gradient squared (CGS) method for solving a nonsymmetric sparse linear system A*x=b.

cg_ne, a MATLAB code which implements the conjugate gradient method (CG) for the normal equations (NE), that is, a method for solving a system of linear equations of the form A*x=b, where the matrix A is not symmetric positive definite (SPD). In this case, it is attempted to set up and solve the normal equations A'*A*x=A'*b.

sor, a MATLAB code which implements a simple version of the successive over-relaxation (SOR) method for the iteration solution of a linear system of equations.

Reference:

  1. William Layton, Myron Sussman,
    Numerical Linear Algebra,
    ISBN13: 978-1-312-32985-0.

Source Code:


Last revised on 01 February 2025.