Infinity norm bounds for the inverse of $ SDD_1^{+} $ matrices with applications

Abstract

A new subclass of nonsingular $ H $-matrix named $ SDD_1^{+} $ matrices is studied in this paper. The relationships between $ SDD_1^{+} $ matrices and other subclasses of nonsingular $ H $-matrices are analyzed by numerical examples. Moreover, the infinity norm bounds of the inverse for $ SDD_1^{+} $ matrices are derived in two different methods. As applications, two error bounds of the linear complementarity problems ($ LCP $) for $ SDD_1^{+} $ matrices are given. Finally, the effectiveness of corresponding results is illustrated by numerical examples.