Abstract
Considered are parametrised linear systems which parameters are subject to tolerances. Rump’s fixed-point iteration method for finding outer and inner approximations of the hull of the solution set is studied and applied to an electrical circuit problem. Interval Gauss-Seidel iteration for parametrised linear systems is introduced and used for improving the enclosures, obtained by the fixed-point method, whenever they are not good enough. Generalised interval arithmetic (on proper and improper intervals) is considered as a computational tool for efficient handling of proper interval problems (to obtain inner interval estimations without inward rounding and to eliminate the dependency problem in parametrised Gauss-Seidel iteration). Numerical results from the application of the above methods to an electrical circuit problem are discussed.
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© 2001 Springer Science+Business Media New York
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Popova, E.D. (2001). On the Solution of Parametrised Linear Systems. In: Krämer, W., von Gudenberg, J.W. (eds) Scientific Computing, Validated Numerics, Interval Methods. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6484-0_11
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DOI: https://doi.org/10.1007/978-1-4757-6484-0_11
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