Open AccessOn unique solvability and Picard’s iterative method for absolute value equations
Author(s) -
Mohamed Achache,
AUTHOR_ID,
Nassima Anane,
AUTHOR_ID
Publication year - 2021
Publication title -
bulletin of the "transilvania" university of braşov. series iii, mathematics and computer science
Language(s) - English
Resource type - Journals
eISSN - 2810-2037
pISSN - 2810-2029
DOI - 10.31926/but.mif.2021.1.63.1.2
Subject(s) - mathematics , complementarity (molecular biology) , convergence (economics) , simple (philosophy) , initial value problem , value (mathematics) , iterative method , mathematical analysis , pure mathematics , mathematical optimization , statistics , philosophy , genetics , epistemology , economics , biology , economic growth
In this paper, we deal with unique solvability and numerical solution ofabsolute value equations (AVE),Ax−B|x|=b, (A,B∈Rn×n,b∈Rn).Under some weaker conditions, a simple proof is given for unique solvabilityof AVE. Furthermore, we demonstrate with an example that these results arereliable to detect unique solvability of AVE. These results are also extendedto unique solvability of standard and horizontal linear complementarity prob-lems. Finally, we suggest a Picard iterative method to compute an approx-imated solution of some uniquely solvable AVE problems where its globallylinear convergence is guaranteed via one of our weaker sufficient condition.