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<p>A new subclass of <i>H</i>-matrices named <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textrm{SDD}_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>SDD</mtext> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-type matrices is introduced. The relationships between <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\textrm{SDD}_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>SDD</mtext> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-type matrices and other subclasses of <i>H</i>-matrices are studied. Moreover, the infinite norm bounds for the inverse of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\textrm{SDD}_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>SDD</mtext> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-type matrices are provided. As applications, error bounds of the linear complementarity problems (LCPs) for <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\textrm{SDD}_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>SDD</mtext> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-type matrices and strictly diagonally dominant (<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\textrm{SDD}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>SDD</mtext> </math></EquationSource> </InlineEquation>) matrices strictly diagonally dominant (are also presented, which improve some existing bounds. Numerical examples are presented to demonstrate the effectiveness of the obtained results.</p>

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Infinity Norm Bounds for the Inverse of \(\textrm{SDD}_1\)-Type Matrices with Applications

  • 期刊论文

  • 发表日期：

    2025年1月17日

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  • Yuanjie Geng,
  • Yuxue Zhu,
  • Fude Zhang,
  • Feng Wang

摘要

A new subclass of H-matrices named \(\textrm{SDD}_1\) SDD 1 -type matrices is introduced. The relationships between \(\textrm{SDD}_1\) SDD 1 -type matrices and other subclasses of H-matrices are studied. Moreover, the infinite norm bounds for the inverse of \(\textrm{SDD}_1\) SDD 1 -type matrices are provided. As applications, error bounds of the linear complementarity problems (LCPs) for \(\textrm{SDD}_1\) SDD 1 -type matrices and strictly diagonally dominant ( \(\textrm{SDD}\) SDD ) matrices strictly diagonally dominant (are also presented, which improve some existing bounds. Numerical examples are presented to demonstrate the effectiveness of the obtained results.