Matrix multisplitting Picard-iterative method for solving generalized absolute value matrix equation

By Mehdi Dehghan, Akbar Shirilord. 2020

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Abstract The absolute value equation appears in various fields of applied mathematics such as operational research. Here we consider its generalized version AX + B | X | = C , where A , B , C ∈ C n × n are given, | X | = ( | x i , j | ) and X ∈ C n × 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 σ min ( A ) > n σ max ( | B | ) , this method is convergent, where σ max ( | B | ) denotes the largest singular value of matrix | B | and σ min ( 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.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/60a9221fd54c02962fbb0435abb1dd94b2348bb6