Abstract
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.
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Skalna, I. (2011). A Comparison of Methods for Solving Parametric Interval Linear Systems with General Dependencies. In: Dimov, I., Dimova, S., Kolkovska, N. (eds) Numerical Methods and Applications. NMA 2010. Lecture Notes in Computer Science, vol 6046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18466-6_59
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DOI: https://doi.org/10.1007/978-3-642-18466-6_59
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