NEKRASOV TYPE MATRICES AND UPPER BOUNDS FOR THEIR INVERSES

摘要

The paper considers the so-called P-Nekrasov and {P1, P2}-Nekrasov matrices, defined in terms of permutation matrices P,P1,P2, which generalize the well-known notion of Nekrasov matrices. For such matrices A, available upper bounds on ‖A~(-1)‖_ ∠are recalled, and new upper bounds for the P-Nekrasov and {P1, P2}-Nekrasov matrices are suggested. It is shown that the latter bound generally improves the earlier bounds, as well as the bound for the inverse of a P-Nekrasov matrix and the classical bound for the inverse of a strictly diagonally dominant matrix.