An iterative algorithm for solving sparse linear equations

ABSTRACT

This article introduces a new iterative technique for solving systems of linear equations of the kind Ax = b. Convergence, and with a given rate, is guaranteed with the square nonsingular matrix A being non-negative. The iterative algorithm depends on a scheme derived from Bayesian updating. The algorithm is shown to compare very favorably with the wisely used GMRES routine. With the algorithm being easy to code, it has the potential to be highly useable.

KEYWORDS:

• Bayesian update
• Iterative algorithm
• Non-negative matrix
• Stochastic matrix

MATHEMATICS SUBJECT CLASSIFICATION:

• 65F10
• 15A06

Acknowledgments

I am grateful for the comments of a reviewer on a previous version of the article.

Notes

1 Scilab is available from www.scilab.org and is open source software for numerical computation.