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2016•Communications in Statistics - Simulation and ComputationRequires access

An iterative algorithm for solving sparse linear equations

Stephen Graham Walker

Open publisher page 3 citations

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.

About this research paper

What this paper is about

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.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Method / approach

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Available 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.

Key concepts: Invertible matrix, Generalized minimal residual method, Algorithm, Iterative method, Computer science, Convergence (economics), Matrix-free methods, Linear system

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