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Published in:
2011 | OriginalPaper | Chapter
A Comparison of Methods for Solving Parametric Interval Linear Systems with General Dependencies
Author : Iwona Skalna
Published in: Numerical Methods and Applications
Publisher: Springer Berlin Heidelberg
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This study compares two methods for solving interval linear systems whose coefficients are functions of interval parameters: the generalized Rump’s fixed-point iteration and Skalna’s Direct Method. Both methods have the same scope of application and require estimating the range of the same functions over a box. Evaluation of functional ranges using the simplest form of interval analysis produces wide intervals. This is due in a large part to the so-called interval dependency. To cope with the dependence problem, revised affine arithmetic with a new affine approximation of a product is used. Numerical examples are provided to show the advantages of Skalna’s Direct Method over generalized Rump’s fixed point iteration.