A new subclass of H-matrices, extended <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$SDD_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>D</mi> <msub> <mi>D</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$ESDD_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mi>S</mi> <mi>D</mi> <msub> <mi>D</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>) matrices, is studied in this paper. The relationship between <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$ESDD_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mi>S</mi> <mi>D</mi> <msub> <mi>D</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> matrices and other subclasses of H-matrices is analyzed, and several properties of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$ESDD_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mi>S</mi> <mi>D</mi> <msub> <mi>D</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> matrices are presented. Moreover, the infinity norm bounds of the inverse of <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$ESDD_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mi>S</mi> <mi>D</mi> <msub> <mi>D</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> matrices are derived, and a new infinity norm bound of the inverse of SDD matrices is provided. As applications, the error bound for the linear complementarity problems (LCP) of <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$ESDD_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mi>S</mi> <mi>D</mi> <msub> <mi>D</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> matrices is given. Finally, the effectiveness of corresponding results are illustrated by numerical examples.

Infinity norm bounds for the inverse of extended $SDD_1$ matrices with applications

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发表日期：

2025年7月7日

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Yuxue Zhu,
Yuanjie Geng,
Feng Wang,
Lanlan Liu

摘要

A new subclass of H-matrices, extended $SDD_1$ $S D D_{1}$ ( $ESDD_1$ $E S D D_{1}$ ) matrices, is studied in this paper. The relationship between $ESDD_1$ $E S D D_{1}$ matrices and other subclasses of H-matrices is analyzed, and several properties of $ESDD_1$ $E S D D_{1}$ matrices are presented. Moreover, the infinity norm bounds of the inverse of $ESDD_1$ $E S D D_{1}$ matrices are derived, and a new infinity norm bound of the inverse of SDD matrices is provided. As applications, the error bound for the linear complementarity problems (LCP) of $ESDD_1$ $E S D D_{1}$ matrices is given. Finally, the effectiveness of corresponding results are illustrated by numerical examples.

Infinity norm bounds for the inverse of extended \(SDD_1\) matrices with applications

摘要