The solution of a type of absolute value equations using two new matrix splitting iterative techniques

Finding the solution of an absolute value vector equation (AVE) of the form Ax-\vert x\vert= b is an important subject in scientific computing, operations research, engineering, management science, and economic applications. This paper proposes two new iterative techniques to solve such AVEs. Both t...

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Bibliographic Details
Published inPortugaliae mathematica Vol. 79; no. 3; pp. 241 - 252
Main Authors Ali, Rashid, Pan, Kejia
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 01.01.2022
Subjects
Absolute value
Fixed point theory
Iterative methods (Mathematics)
Matrices
China
Online AccessGet full text
ISSN0032-5155
1662-2758
1662-2758
DOI10.4171/pm/2089

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Summary:Finding the solution of an absolute value vector equation (AVE) of the form Ax-\vert x\vert= b is an important subject in scientific computing, operations research, engineering, management science, and economic applications. This paper proposes two new iterative techniques to solve such AVEs. Both techniques are based on a decomposition of the coefficient matrix and a fixed-point principle. The convergence of the proposed techniques under appropriate assumptions is examined. We present results of numerical simulations to verify our theoretical findings and demonstrate the efficiency of our techniques.
ISSN:0032-5155
1662-2758
1662-2758
DOI:10.4171/pm/2089