Abstract
The absolute value equation appears in various fields of applied mathematics such as operational research. Here we consider its generalized versionAX+B|X|=C, where A,B,C∈Cn×n are given, |X|=(|xi,j|) and X∈Cn×n is an unknown matrix that must be determined. In this investigation, based on the Picard matrix splitting iteration method, we applied a matrix splitting method for solving it. We will see that under the condition σmin(A)>nσmax(|B|), this method is convergent, where σmax(|B|) denotes the largest singular value of matrix |B| and σmin(A) denotes the smallest singular value of matrix A. Then we give some convergence theorems for our new method and analyze this procedure in detail. Then we consider a p-step iteration method for solving this equation and analyze this procedure. Numerical experiment results show the efficiency of the method.
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