Solving linear systems whose input data are rational functions of interval parameters

Authors:
Evgenija D. Popova
Affiliations:
Institute of Mathematics & Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
Venue:
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Year:
2006

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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.