NDLI: A note on estimating the error in Gaussian elimination without pivoting

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A note on estimating the error in Gaussian elimination without pivoting

Content Provider	ACM Digital Library
Author	George, Alan Chu, Eleanor
Abstract	This article deals with the problem of estimating the error in the computed solution to a system of equations when that solution is obtained by using Gaussian elimination without pivoting. The corresponding problem, where either partial or complete pivoting is used, has received considerable attention, and efficient and reliable methods have been developed. However, in the context of solving large sparse systems, it is often very attractive to apply Gaussian elimination without pivoting, even though it cannot be guaranteed a-priori that the computation is numerically stable. When this is done, it is important to be able to determine when serious numerical errors have occurred, and to be able to estimate the error in the computed solution. In this paper a method for achieving this goal is described. Results of a large number of numerical experiments suggest that the method is both inexpensive and reliable.
Starting Page	2
Ending Page	7
Page Count	6
File Format	PDF
ISSN	01635778
DOI	10.1145/1057941.1057942
Journal	ACM SIGNUM Newsletter (SGNM)
Volume Number	20
Issue Number	2
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1990-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article

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