cgne

cgne, a MATLAB code which implements the conjugate gradient method (CG) for the normal equations, 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.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

cgne is available in a MATLAB version.

Related Data and Programs:

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.

cgne_test

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

Reference:

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

Source Code:

• cgne.m, carries out the CGNE algorithm.
• helmert_matrix.m, returns the Helmert matrix.
• invol_matrix.m, returns the involutary matrix.
• lesp_matrix.m, returns the Lesp matrix.