Paper Info
Title
An algorithm for automatically selecting a suitable verification method for linear systems
Abstract
Several methods have been proposed to calculate a rigorous error bound of an approximate solution of a linear system by floating-point arithmetic. These methods are called `verification methods'. Applicable range of these methods are different. It depends mainly on the condition number and the dimension of the coefficient matrix whether such methods succeed to work or not. In general, however, the condition number is not known in advance. If the dimension or the condition number is large to some extent, then Oishi---Rump's method, which is known as the fastest verification method for this purpose, may fail. There are more robust verification methods whose computational cost is larger than the Oishi---Rump's one. It is not so efficient to apply such robust methods to well-conditioned problems. The aim of this paper is to choose a suitable verification method whose computational cost is minimum to succeed. First in this paper, four fast verification methods for linear systems are briefly reviewed. Next, a compromise method between Oishi---Rump's and Ogita---Oishi's one is developed. Then, an algorithm which automatically and efficiently chooses an appropriate verification method from five verification methods is proposed. The proposed algorithm does as much work as necessary to calculate error bounds of approximate solutions of linear systems. Finally, numerical results are presented.
Year
DOI
Venue
2011
10.1007/s11075-010-9389-6
Numerical Algorithms
Keywords
Field
DocType
Linear systems,Verified computation
Condition number,Mathematical optimization,Coefficient matrix,Linear system,Algorithm,Runtime verification,Approximate solution,Mathematics
Journal
Volume
Issue
ISSN
56
3
1017-1398
Citations 
PageRank 
References 
1
0.41
3
Authors
3
Name
Order
Citations
PageRank
Katsuhisa Ozaki1134.70
Takeshi Ogita223123.39
Shin'ichi Oishi328037.14