Index-proper nonnegative splittings of matrices

Abstract

The theory of splitting is a useful tool for finding solution of a system of linear equations. Many woks are going on for singular system of linear equations. In this article, we have introduced a new splitting called indexproper nonnegative splitting for singular square matrices. Several convergence and comparison results are also established. We then apply the same theory to double splitting.

Three-step alternating iterations for index 1 and non-singular matrices

“…However, the iteration scheme (2) converges very slow in many practical cases. To overcome this, several comparison results are proposed in the literature (see [9], [13], [14], [15] and [34] and the references cited therein). In case of a matrix having many proper splittings, comparison results are not so useful to find the best splitting (in the sense that the iteration matrix arising from a matrix splitting has the smallest spectral radius).…”