Open AccessError bounds for complementarity problems with tridiagonal nonlinear functions
Author(s) -
G. Alefeld,
Ze Wang
Publication year - 2008
Publication title -
computing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.409
H-Index - 60
eISSN - 1436-5057
pISSN - 0010-485X
DOI - 10.1007/s00607-008-0021-8
Subject(s) - tridiagonal matrix , discretization , mathematics , nonlinear complementarity problem , complementarity (molecular biology) , nonlinear system , mixed complementarity problem , tridiagonal matrix algorithm , complementarity theory , boundary value problem , discretization error , numerical analysis , eigenvalues and eigenvectors , mathematical analysis , physics , genetics , biology , quantum mechanics
In this paper we consider the complementarity problem NCP(f) with f(x) = Mx + φ( x), where M ∈ R n×n is a real matrix and φ is a so-called tridiagonal (nonlinear) mapping. This problem occurs, for example, if certain classes of free boundary problems are discretized. We compute error bounds for approximations to a solution x* of the discretized problems. The error bounds are improved by an iterative method and can be made arbitrarily small. The ideas are illustrated by numerical experiments.
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