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<p>In this article, we propose a new combining real and imaginary parts iterative method, commonly known as the NCRI method, to more effectively solve large sparse complex linear systems of equations. We establish an upper bound of the spectral radius of the iteration matrix using the NQCRI iteration method, and analyzed the range of parameters <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation> when the upper bound is less than 1. In addition, we provide the values of parameters <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation> that minimize the upper bound of the spectral radius of the iterative matrix in the NCRI iteration method. In order to reduce the computational cost of the NCRI method, we establish inexact NCRI (INCRI) iteration method and provide their convergence properties. Lastly, several numerical examples are used to further prove that the our methods are effective and feasible.</p>

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New combining real and imaginary parts iteration method for linear systems

  • 期刊论文

  • 发表日期：

    2025年6月29日

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  • Beibei Li,
  • Heping Ma,
  • Na Kui,
  • Xuechuan Sun

摘要

In this article, we propose a new combining real and imaginary parts iterative method, commonly known as the NCRI method, to more effectively solve large sparse complex linear systems of equations. We establish an upper bound of the spectral radius of the iteration matrix using the NQCRI iteration method, and analyzed the range of parameters \(\alpha \) α and \(\omega \) ω when the upper bound is less than 1. In addition, we provide the values of parameters \(\alpha \) α and \(\omega \) ω that minimize the upper bound of the spectral radius of the iterative matrix in the NCRI iteration method. In order to reduce the computational cost of the NCRI method, we establish inexact NCRI (INCRI) iteration method and provide their convergence properties. Lastly, several numerical examples are used to further prove that the our methods are effective and feasible.