Improved solution enclosures for over- and underdetermined interval linear systems

Authors:
Evgenija D. Popova
Affiliations:
Inst. of Mathematics & Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
Venue:
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Year:
2005

Citing 4
Cited 1

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The Mathematica book (4th edition)

The Mathematica book (4th edition)
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)

Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)

Fast enclosure for solutions in underdetermined systems

Journal of Computational and Applied Mathematics

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Abstract

In this paper we discuss an inclusion method for solving rectangular (over- and under-determined) dense linear systems where the input data are uncertain and vary within given intervals. An improvement of the quality of the solution enclosures is described for both independent and parameter dependent input intervals. A fixed-point algorithm with result verification that exploits the structure of the problems to be solved is given. Mathematica functions for solving the discussed rectangular problems are developed and presented. Numerical examples illustrate the advantages of the proposed improved approach.