AN OPTIMUM PARTITION FOR INVERTING A NONSINGULAR MATRIX

Abstract

A new strategy for inverting a nonsingular matrix is evaluated in this paper. The essential concept of this strategy is to partition a nonsingular matrix into blocks, then to apply the author's decomposition to the block-based procedure. Since different partitions require different costs, finding an economical partition is necessary. This paper studies the optimum partition so that the complexity for the inverse of a nonsingular matrix may be significantly reduced.