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<p>Iteration solvers based on matrix splittings are essential for large sparse linear systems. Recently, Bai (<CitationRef CitationID="CR6">2024b</CitationRef>) proposed a single-step matrix splitting iteration (SMSI) paradigm incorporating multiple relaxation parameters, which offers a flexible framework. This work establishes rigorous and general convergence criteria for the SMSI method applied to Hermitian positive definite coefficient matrices. Our results significantly broaden the theoretical applicability of this paradigm. Comprehensive numerical experiments demonstrate the superior efficiency of the SMSI method compared to existing iteration solvers.</p>

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Convergence of the single-step matrix splitting iteration paradigm for Hermitian positive definite linear systems

  • 期刊论文

  • 发表日期：

    2025年9月18日

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  • Hong-Yu Wu

摘要

Iteration solvers based on matrix splittings are essential for large sparse linear systems. Recently, Bai (2024b) proposed a single-step matrix splitting iteration (SMSI) paradigm incorporating multiple relaxation parameters, which offers a flexible framework. This work establishes rigorous and general convergence criteria for the SMSI method applied to Hermitian positive definite coefficient matrices. Our results significantly broaden the theoretical applicability of this paradigm. Comprehensive numerical experiments demonstrate the superior efficiency of the SMSI method compared to existing iteration solvers.