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Super-fast validated solution of linear systems
Publikationstyp
Journal Article
Date Issued
2006-02-17
Sprache
English
Author(s)
Institut
TORE-URI
Volume
199
Issue
2
Start Page
199
End Page
206
Citation
Journal of Computational and Applied Mathematics 199 (2): 199-206 (2007)
Publisher DOI
Scopus ID
Publisher
North-Holland
Validated solution of a problem means to compute error bounds for a solution in finite precision. This includes the proof of existence of a solution. The computed error bounds are to be correct including all possible effects of rounding errors. The fastest known validation algorithm for the solution of a system of linear equations requires twice the computing time of a standard (purely) numerical algorithm. In this paper we present a super-fast validation algorithm for linear systems with symmetric positive definite matrix. This means that the entire computing time for the validation algorithm including computation of an approximated solution is the same as for a standard numerical algorithm. Numerical results are presented.
Subjects
INTLAB
Self-validating methods
Sparse linear systems
Verified error bounds
DDC Class
004: Informatik