Abstract
The paper proposes an approach for self-verified solving of linear systems involving rational dependencies between interval parameters. A general inclusion method is combined with an interval arithmetic technique providing inner and outer bounds for the range of monotone rational functions. The arithmetic on proper and improper intervals is used as an intermediate computational tool for eliminating the dependency problem in range computation and for obtaining inner estimations by outwardly rounded interval arithmetic. Supporting software tools with result verification, developed in the environment of CAS Mathematica, are reported.
This work was supported by the Bulgarian National Science Fund under grant No. MM-1301/03.
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Popova, E.D. (2007). Solving Linear Systems Whose Input Data Are Rational Functions of Interval Parameters. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_41
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DOI: https://doi.org/10.1007/978-3-540-70942-8_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70940-4
Online ISBN: 978-3-540-70942-8
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