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References (23)
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Xiaomei Yang (1964)
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The (B3) bound is obtained from the (B2) bound by taking C = A -~. The (B3) bound can be written as II x -y II -< N A-1 II -
The (B2) upper bound is obtained from the (B4) upper bound since I I Cr fl <- licIlllrll -
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How to determine accuracy of the output of a matrix inversion programJournal of Research of the National Bureau of Standards, Section B: Mathematical Sciences
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ACKNOWLEDGMENTS For many valuable suggestions we thank J. R. Rice and the referees of TOMS -
B1) bound on II'N.. 1.1(+6) 2.5(+6) 2.5 -
(1975)
ACM Transactions on Mathematical Software -
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- Publisher
- Association for Computing Machinery
- Copyright
- Copyright © 1975 by ACM Inc.
- ISSN
- 0098-3500
- DOI
- 10.1145/355644.355648
- Publisher site
- See Article on Publisher Site
Abstract
Computable Accurate Upper and Lower Error Bounds for Approximate Solutions of Linear Algebraic Systems T.J. AIRD International Mathematical and Statistical Libraries, Inc. and ROBERT E. LYNCH Purdue University Six bounds are considered on a norm of x - y, where x is the solution of a nonsingular linear system, A x --- b, and where y is an estimate of x. Methods are described for computing one of these. [[Crll/(1-k T) < [ I x - yll <-- [[ Cr [ [ / ( 1 - T) < ( l + T ) / ( 1 - - T ) [ I x - - y l l i f T = IICA -I[[ < 1, where C "~ A-1 and r = b - A y . In addition to supplying upper and lower bounds, this gives very accurate error estimates which are orders of magnitude smaller than those obtained from other bounds. Key Words and Phrases: error bounds, linear algebraic systems, computational techniques, numerical experimental results, high speed digital computation, approximate solutions, norms, eigenvalue problems, least squares CR Categorms: 4.6, 5.11, 5.14 1. ERROR BOUNDS A p r i o r i b o u n
Journal
ACM Transactions on Mathematical Software (TOMS) – Association for Computing Machinery
Published: Sep 1, 1975