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Abstract <p>In this paper, we introduce a new subclass of <i>P</i>-matrices called <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({{B}_{k}}\)</EquationSource> <!--ComMat2570209Sun-m1--> </InlineEquation>-matrices, which contains <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(B\)</EquationSource> <!--ComMat2570209Sun-m2--> </InlineEquation>-matrices and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({{B}_{1}}\)</EquationSource> <!--ComMat2570209Sun-m3--> </InlineEquation>-matrices, propose some properties of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({{B}_{k}}\)</EquationSource> <!--ComMat2570209Sun-m4--> </InlineEquation>-matrices, and analyze the relationships among <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({{B}_{k}}\)</EquationSource> <!--ComMat2570209Sun-m5--> </InlineEquation>-matrices and other matrices. Moreover, we derive two infinity norm upper bounds of the inverse for <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\({{B}_{k}}\)</EquationSource> <!--ComMat2570209Sun-m6--> </InlineEquation>-matrices. Furthermore, based on new infinity norm bounds, we present error bounds for the linear complementarity problems of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\({{B}_{k}}\)</EquationSource> <!--ComMat2570209Sun-m7--> </InlineEquation>-matrices. Numerical examples show that the obtained results can improve some existing bounds.</p>

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Bk-Matrices and Error Bounds for the Linear Complementarity Problems

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Deshu Sun,
  • Qin Li

摘要

Abstract

In this paper, we introduce a new subclass of P-matrices called \({{B}_{k}}\) -matrices, which contains \(B\) -matrices and \({{B}_{1}}\) -matrices, propose some properties of \({{B}_{k}}\) -matrices, and analyze the relationships among \({{B}_{k}}\) -matrices and other matrices. Moreover, we derive two infinity norm upper bounds of the inverse for \({{B}_{k}}\) -matrices. Furthermore, based on new infinity norm bounds, we present error bounds for the linear complementarity problems of \({{B}_{k}}\) -matrices. Numerical examples show that the obtained results can improve some existing bounds.