In this paper, we investigate a new subclass of H-matrices, termed weakly <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$SDD_1^\dagger $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mn>1</mn> <mo>†</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation> (for shortly, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$WSDD_1^\dagger $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mn>1</mn> <mo>†</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation>) matrices, and explore the relationships between <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$WSDD_1^\dagger $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mn>1</mn> <mo>†</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation> matrices and other subclasses of H-matrices. Based on the algebraic properties of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$WSDD_1^\dagger $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mn>1</mn> <mo>†</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation> matrices, the infinity norm upper bound for the inverse of <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$WSDD_1^\dagger $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mn>1</mn> <mo>†</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation> matrices is established, and several sufficient conditions are provided to ensure that the k-subdirect sum of two <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$WSDD_1^\dagger $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mi>S</mi> <mi>D</mi> <msubsup> <mi>D</mi> <mn>1</mn> <mo>†</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation> matrices still belongs to the same matrix class. Furthermore, numerical examples are presented to illustrate the corresponding results.

Weakly $SDD_1^\dagger $ matrices with applications

期刊论文
发表日期：

2026年2月16日

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Zongxue Hu,
Lv Yang,
Feng Wang,
Lanlan Liu

摘要

In this paper, we investigate a new subclass of H-matrices, termed weakly $SDD_1^\dagger $ $S D D_{1}^{†}$ (for shortly, $WSDD_1^\dagger $ $W S D D_{1}^{†}$ ) matrices, and explore the relationships between $WSDD_1^\dagger $ $W S D D_{1}^{†}$ matrices and other subclasses of H-matrices. Based on the algebraic properties of $WSDD_1^\dagger $ $W S D D_{1}^{†}$ matrices, the infinity norm upper bound for the inverse of $WSDD_1^\dagger $ $W S D D_{1}^{†}$ matrices is established, and several sufficient conditions are provided to ensure that the k-subdirect sum of two $WSDD_1^\dagger $ $W S D D_{1}^{†}$ matrices still belongs to the same matrix class. Furthermore, numerical examples are presented to illustrate the corresponding results.

Weakly \(SDD_1^\dagger \) matrices with applications

摘要