Abstract
We study the dominant degree for Schur complement of S-strictly diagonally dominant matrix and its applications in reducing the order for the solution of large-scale linear systems and the linear complementarity problems. Based on the proposed dominant degree, we obtain an infinite norm bound for the inverse matrix of the Schur complement, and then derive an infinite norm bound for the original matrix. We also give the eigenvalue inclusion set for the Schur complement. In addition, we present a new error bound for the linear complementarity problem with an SB-matrix, which improves the existing results when the dominant degree is tiny. A series of numerical experiments with lots of random matrices are presented to show the efficiency and superiority of our results.
Published Version
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