pcg.m with 'null' and 'flex' options

Preconditioned Conjugate Gradients handles homogeneous equations and nonsymmetric preconditioning
Updated 15 May 2015

View License

PCG Preconditioned Conjugate Gradients Method is a replacement of the standard built-in PCG code. Two new options are implemented: 'flex' and 'null'. The 'flex' option changes the standard PCG algorithm into the flexible one. It allows using sophisticated preconditioning, not limited to the traditional fixed SPD preconditioners, as required by the standard PCG.
With the 'null' option, the code attempts to compute a nontrivial solution X of the homogeneous system of linear equations A*X=0. Here, the coefficient matrix A must be Hermitian and positive semi-definite. If the null-space of A is more than one dimensional, i.e. A*X=0 allows multiple linear independent solutions, the code still converges to one solution, namely, the projection of the initial guess to the null-space.

Without the new options, the new PCG code works exactly the same way as the latest revision of the built-in PCG.

Cite As

Andrew Knyazev (2024). pcg.m with 'null' and 'flex' options (https://www.mathworks.com/matlabcentral/fileexchange/50-pcg-m-with-null-and-flex-options), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R11
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes

Updated to work with the latest MATLAB. Made compatible with the built-in PCG. Implemented the new option 'flex' to turn the standard PCG into flexible, Added new examples in the header.
added a conversion to a toolbox