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<p>The conjugate gradient (CG) method is specifically designed for solving symmetric positive definite (SPD) linear systems. However, when addressing linear systems with an indefinite matrix, a category of algorithms known as Planar algorithms comes into play. One notable member of these Planar CG algorithms is the FLR algorithm. The FLR algorithm paved the way for the introduction of two simplified and more cost-effective algorithms, namely the Alg-F and Alg-ML algorithms. The focus of this article is to incorporate the <i>s</i>-step technique into these three aforementioned algorithms, enabling the adjustment of the parameter <i>s</i> in each iteration. Through the execution of several numerical tests, the performance outcomes of these algorithms are systematically compared.</p>

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Variable s-step technique for Planar algorithms in solving indefinite linear systems

  • 期刊论文

  • 发表日期：

    2025年6月2日

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  • Hojjatollah Shokri Kaveh,
  • Masoud Hajarian,
  • Anthony T. Chronopoulos

摘要

The conjugate gradient (CG) method is specifically designed for solving symmetric positive definite (SPD) linear systems. However, when addressing linear systems with an indefinite matrix, a category of algorithms known as Planar algorithms comes into play. One notable member of these Planar CG algorithms is the FLR algorithm. The FLR algorithm paved the way for the introduction of two simplified and more cost-effective algorithms, namely the Alg-F and Alg-ML algorithms. The focus of this article is to incorporate the s-step technique into these three aforementioned algorithms, enabling the adjustment of the parameter s in each iteration. Through the execution of several numerical tests, the performance outcomes of these algorithms are systematically compared.