Matrix multisplitting Picard-iterative method for solving generalized absolute value matrix equation
2020; Elsevier BV; Volume: 158; Linguagem: Inglês
10.1016/j.apnum.2020.08.001
ISSN1873-5460
AutoresMehdi Dehghan, Akbar Shirilord,
Tópico(s)Iterative Methods for Nonlinear Equations
ResumoThe 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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