A new subclass of nonsingular H-matrices named <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$GSDD_1^{}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mn>1</mn> <mrow> <mrow /> <mo>∗</mo> <mrow /> <mo>∗</mo> </mrow> </msubsup> </mrow> </math></EquationSource> </InlineEquation> matrices is studied in this paper. The relationship between <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$GSDD_1^{}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mn>1</mn> <mrow> <mrow /> <mo>∗</mo> <mrow /> <mo>∗</mo> </mrow> </msubsup> </mrow> </math></EquationSource> </InlineEquation> matrices and other subclass of nonsingular H-matrices is discussed by numerical examples. Moreover, the infinity norm bounds for the inverse of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$GSDD_1^{}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mn>1</mn> <mrow> <mrow /> <mo>∗</mo> <mrow /> <mo>∗</mo> </mrow> </msubsup> </mrow> </math></EquationSource> </InlineEquation> matrices are given, and the effectiveness of the corresponding results are illustrated by numerical examples. Finally, based on the definition of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$GSDD_1^{}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mn>1</mn> <mrow> <mrow /> <mo>∗</mo> <mrow /> <mo>∗</mo> </mrow> </msubsup> </mrow> </math></EquationSource> </InlineEquation> matrices, a new subclass of P-matrices, which is called a <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$GB_1^{}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <msubsup> <mi>B</mi> <mn>1</mn> <mrow> <mrow /> <mo>∗</mo> <mrow /> <mo>∗</mo> </mrow> </msubsup> </mrow> </math></EquationSource> </InlineEquation>-matrix, is proposed, and also the relationship between <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$GB_1^{}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <msubsup> <mi>B</mi> <mn>1</mn> <mrow> <mrow /> <mo>∗</mo> <mrow /> <mo>∗</mo> </mrow> </msubsup> </mrow> </math></EquationSource> </InlineEquation>-matrices and other subclass of P-matrices is analyzed.

A new generalization of $SDD_1$ matrices

期刊论文
发表日期：

2026年4月1日

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Xiaoyong Chen,
Weiting Duan,
Min Hui,
Yaqiang Wang

摘要

A new subclass of nonsingular H-matrices named $GSDD_1^{**}$ $G S D D_{1}^{* *}$ matrices is studied in this paper. The relationship between $GSDD_1^{**}$ $G S D D_{1}^{* *}$ matrices and other subclass of nonsingular H-matrices is discussed by numerical examples. Moreover, the infinity norm bounds for the inverse of $GSDD_1^{**}$ $G S D D_{1}^{* *}$ matrices are given, and the effectiveness of the corresponding results are illustrated by numerical examples. Finally, based on the definition of $GSDD_1^{**}$ $G S D D_{1}^{* *}$ matrices, a new subclass of P-matrices, which is called a $GB_1^{**}$ $G B_{1}^{* *}$ -matrix, is proposed, and also the relationship between $GB_1^{**}$ $G B_{1}^{* *}$ -matrices and other subclass of P-matrices is analyzed.

A new generalization of \(SDD_1\) matrices

摘要