Parametric Linear System of Equations, Whose Elements are Nonlinear Functions

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SCAN '06 Proceedings of the 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
Year:
2006

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Abstract

This paper addresses the problem of solving parametric linear systems of equations whose coefficients are, in the general case, nonlinear functions of interval parameters. Such systems, are encountered in many practical problems, e.g in electrical engineering and mechanical systems. A C-XSC[8] implementation of a parametric fixed-point iteration method for computing an outer enclosure for the solution set is proposed in this paper. Numerical examples illustrating the applicability of the proposed method are solved, and compared with other methods. Keywords: parametric linear systems, validated interval software, C-XSC, nonlinear functions, Generalized Interval Arithmetic.