Error bounds for linear complementarity problems of SDD₁ matrices and SDD₁-B matrices

Abstract

An upper bound of the infinity norm for the inverse of $ SD{D_1} $ matrix is presented. We apply the new bound to linear complementarity problems (LCPs) and obtain an alternative error bound for LCPs of $ SD{D_1} $ matrices and $ SD{{D}_{1}} $-$ B $ matrices. In addition, a new lower bound for the smallest singular value is also given. Numerical examples show the validity of the results.

Keywords

• error bounds
• linear complementarity problems
• infinity norm
• sdd₁ matrices
• sdd₁-b matrices
• singular values