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<p>Inspired by the idea of the single step iteration method, we establish the double parameter single step (DPSS) and new single step (NSS) iteration methods for solving the complex symmetric linear systems. We present the upper bounds of the spectral radii of iteration matrices of the two new methods and give the parameters convergence intervals where the upper bounds are less than 1. In addition, the theoretical quasi-optimal parameters minimizing the upper bounds of the spectral radius of the iteration matrices of the DPSS and NSS methods are also given. Finally, we compare the numerical performances of the new methods with those of some existing ones by some tested examples, which illustrate the effectiveness of our methods.</p>

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New single step iteration methods for linear systems with complex symmetric positive definite coefficient matrices

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Beibei Li,
  • Zhengge Huang,
  • Jingjing Cui

摘要

Inspired by the idea of the single step iteration method, we establish the double parameter single step (DPSS) and new single step (NSS) iteration methods for solving the complex symmetric linear systems. We present the upper bounds of the spectral radii of iteration matrices of the two new methods and give the parameters convergence intervals where the upper bounds are less than 1. In addition, the theoretical quasi-optimal parameters minimizing the upper bounds of the spectral radius of the iteration matrices of the DPSS and NSS methods are also given. Finally, we compare the numerical performances of the new methods with those of some existing ones by some tested examples, which illustrate the effectiveness of our methods.