Douglas-Rachford iterations for the HSS splitting

Abstract In this paper, we study a variation of the HSS Iteration method. This variation is based on a method introduced by Douglas and Rachford and has been called the Douglas-Rachford iterative method throughout the literature. A convergence criteria is given for positive definite matrices which is similar to the convergence criteria for the HSS iterative method. Examples are given to illustrate numerical differences of these two iterative methods.

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Publication Details

Journal
Numerical Algorithms
Published
2026-04-14
DOI
https://doi.org/10.1007/s11075-026-02373-0
Primary Topic
Iterative Methods for Nonlinear Equations
Type
article
Field-Weighted Citation Impact
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article

Douglas-Rachford iterations for the HSS splitting

Thomas Smotzer, John J. Buoni
Numerical Algorithms
Iterative Methods for Nonlinear Equations
article

Douglas-Rachford iterations for the HSS splitting

Thomas Smotzer, John J. Buoni
article en

Abstract

Abstract In this paper, we study a variation of the HSS Iteration method. This variation is based on a method introduced by Douglas and Rachford and has been called the Douglas-Rachford iterative method throughout the literature. A convergence criteria is given for positive definite matrices which is similar to the convergence criteria for the HSS iterative method. Examples are given to illustrate numerical differences of these two iterative methods.

Numerical Algorithms
Youngstown State University (US)
Reduced inequalities
Openalex Percentile: Top 5%
Iterative Methods for Nonlinear Equations
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