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Generalized $$SDD_k^*$$ matrices and error bounds for linear complementarity problems
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DOI：10.1007/s40314-026-03806-1.png)
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Abstract
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In this paper, we introduce a new subclass of H-matrices, termed generalized $$SDD^{*}_k$$ (abbreviated as $$GSDD_k^*$$ ) matrices, as an extension of the class of $$SDD_k$$ matrices. The relationships between $$GSDD_k^*$$ matrices and other subclasses of H-matrices are analyzed. Moreover, the infinity norm bounds for the inverse of $$GSDD_k^*$$ matrices are provided. Based on existing and new bounds, error bound estimates for the linear complementarity problems associated with $$SDD_k$$ and $$GSDD_k^*$$ matrices are presented. Numerical examples, including quantitative comparisons with existing results, demonstrate that the proposed results outperform several existing bounds in the literature.
Keywords:
\(GSDD_k^*\) matrices
\(SDD_k\) matrices
H-matrices
Infinity norm bounds
Error bound
Linear complementarity problems
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