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<p>In this paper, we introduce a new subclass of <i>H</i>-matrices called <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(N_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-matrices, discuss the relationship between <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(N_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-matrices and other subclasses of <i>H</i>-matrices, present an error bound for the linear complementarity problems of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(N_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-matrices. Moreover, we propose a new subclass of <i>P</i>-matrices named <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(BN_1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>B</mi> <msub> <mi>N</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>-matrices and provide an error bound for the linear complementarity problems of <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(BN_1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>B</mi> <msub> <mi>N</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>-matrices. Numerical examples show the sharpness and applicability of the bounds.</p>

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Error bounds for the linear complementarity problems of \(N_1\)-matrices and \(BN_1\)-matrices

  • 期刊论文

  • 发表日期：

    2025年7月17日

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  • Guixiang Sun,
  • Feng Wang

摘要

In this paper, we introduce a new subclass of H-matrices called \(N_1\) N 1 -matrices, discuss the relationship between \(N_1\) N 1 -matrices and other subclasses of H-matrices, present an error bound for the linear complementarity problems of \(N_1\) N 1 -matrices. Moreover, we propose a new subclass of P-matrices named \(BN_1\) B N 1 -matrices and provide an error bound for the linear complementarity problems of \(BN_1\) B N 1 -matrices. Numerical examples show the sharpness and applicability of the bounds.