In this paper, we introduce a new subclass of H-matrices, termed generalized <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$SDD^{}_k$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mi>k</mi> <mrow> <mrow /> <mo>∗</mo> </mrow> </msubsup> </mrow> </math></EquationSource> </InlineEquation> (abbreviated as <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$GSDD_k^$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mi>k</mi> <mo>∗</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation>) matrices, as an extension of the class of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$SDD_k$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>D</mi> <msub> <mi>D</mi> <mi>k</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> matrices. The relationships between <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$GSDD_k^$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mi>k</mi> <mo>∗</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation> matrices and other subclasses of H-matrices are analyzed. Moreover, the infinity norm bounds for the inverse of <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$GSDD_k^$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mi>k</mi> <mo>∗</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation> matrices are provided. Based on existing and new bounds, error bound estimates for the linear complementarity problems associated with <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$SDD_k$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>D</mi> <msub> <mi>D</mi> <mi>k</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$GSDD_k^*$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mi>k</mi> <mo>∗</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation> matrices are presented. Numerical examples, including quantitative comparisons with existing results, demonstrate that the proposed results outperform several existing bounds in the literature.

Generalized $SDD_k^*$ matrices and error bounds for linear complementarity problems

期刊论文
发表日期：

2026年5月25日

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Zongxue Hu,
Feng Wang,
Lanlan Liu

摘要

In this paper, we introduce a new subclass of H-matrices, termed generalized $SDD^{*}_k$ $S D D_{k}^{*}$ (abbreviated as $GSDD_k^*$ $G S D D_{k}^{*}$ ) matrices, as an extension of the class of $SDD_k$ $S D D_{k}$ matrices. The relationships between $GSDD_k^*$ $G S D D_{k}^{*}$ matrices and other subclasses of H-matrices are analyzed. Moreover, the infinity norm bounds for the inverse of $GSDD_k^*$ $G S D D_{k}^{*}$ matrices are provided. Based on existing and new bounds, error bound estimates for the linear complementarity problems associated with $SDD_k$ $S D D_{k}$ and $GSDD_k^*$ $G S D D_{k}^{*}$ matrices are presented. Numerical examples, including quantitative comparisons with existing results, demonstrate that the proposed results outperform several existing bounds in the literature.

Generalized \(SDD_k^*\) matrices and error bounds for linear complementarity problems

摘要