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Bounding the error for approximate solutions of almost linear complementarity problems using feasible vectors
Author(s) -
Alefeld Götz,
Wang Zhengyu
Publication year - 2011
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.719
Subject(s) - bounding overwatch , mathematics , linear complementarity problem , complementarity (molecular biology) , mathematical optimization , solution set , complementarity theory , set (abstract data type) , upper and lower bounds , computer science , mathematical analysis , nonlinear system , artificial intelligence , biology , genetics , programming language , physics , quantum mechanics
In this paper we use the concept of a feasible vector in order to bound a solution x * of an almost linear complementarity problem in a certain set. This set delivers also componentwise error bounds for an approximation to a solution x *. In the special case that the problem is defined by a so‐called H‐matrix, we prove that the error bounds are more accurate than the corresponding bounds recently obtained. By numerical examples it will be demonstrated that the new bounds can be better by several orders of magnitude. Copyright © 2010 John Wiley & Sons, Ltd.