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We consider a class of iterative methods based on block splitting (BBS) to solve absolute value equationsA⁢x-|x|=bAx-\lvert x\rvert=b. Recently, several works were devoted to deriving sufficient conditions for the convergence of iterative methods of this type under certain assumptions includingν:=∥A-1∥&lt;1\nu:=\lVert A^{-1}\rVert&lt;1. However, the BBS-type iterative methods tend to converge slowly when  is very close to one (i.e.,ν≈1\nu\approx 1). In this paper, using an auxiliary matrix, we develop a new approach by first rewriting the main problem into a new equivalent block system having shifted(1,1)(1,1)-block and then constructing a fixed point iteration. The exploited strategy can significantly improve the convergence speed of the BBS-type iterative methods whenν≈1\nu\approx 1. Numerical experiments are reported to demonstrate the superiority of the new modified iterative scheme over the existing original form of BBS-type methods in the literature.

An Improvement on a Class of Fixed Point Iterative Methods for Solving Absolute Value Equations