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<p>The infinity norm for the inverse of nonsingular <i>H</i>-matrices plays a crucial role in the field of scientific computing. In this paper, we introduce a new class of matrices, called <i>S</i>-Nekrasov type matrices, and demonstrate that they form a distinct subclass of nonsingular <i>H</i>-matrices. Additionally, we present two infinity norm bounds for the inverse of <i>S</i>-Nekrasov type matrices, which improve the well-known Varah’s bound for strictly diagonally dominant matrices. We also use these bounds to derive an error bound for linear complementarity problems involving <i>S</i>-Nekrasov type matrices. Numerical examples are provided to illustrate the effectiveness of these results.</p>

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Infinity norm bounds for the inverse of S-Nekrasov type matrices and their applications

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Lei Gao,
  • Tianyuan Li,
  • Qiuyu Ma

摘要

The infinity norm for the inverse of nonsingular H-matrices plays a crucial role in the field of scientific computing. In this paper, we introduce a new class of matrices, called S-Nekrasov type matrices, and demonstrate that they form a distinct subclass of nonsingular H-matrices. Additionally, we present two infinity norm bounds for the inverse of S-Nekrasov type matrices, which improve the well-known Varah’s bound for strictly diagonally dominant matrices. We also use these bounds to derive an error bound for linear complementarity problems involving S-Nekrasov type matrices. Numerical examples are provided to illustrate the effectiveness of these results.