Round-off error analysis of iterations for large linear systems |
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Authors: | H Woźniakowski |
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Institution: | (1) Department of Computer Science, Carnegie-Mellon University, 15213 Pittsburgh, PA, USA;(2) Present address: Department of Mathematics, University of Warsaw, P.K.i.N. 850, 8p., 00-901 Warsaw, Poland |
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Abstract: | Summary We deal with the rounding error analysis of successive approximation iterations for the solution of large linear systemsA
x
=b. We prove that Jacobi, Richardson, Gauss-Seidel and SOR iterations arenumerically stable wheneverA=A
*>0 andA has PropertyA. This means that the computed resultx
k
approximates the exact solution with relative error of order A·A
–1 where is the relative computer precision. However with the exception of Gauss-Seidel iteration the residual vector Ax
k
–b is of order A2 A
–1 and hence the remaining three iterations arenot well-behaved.This work was partly done during the author's visit at Carnegie-Mellon University and it was supported in part by the Office of Naval Research under Contract N00014-76-C-0370; NR 044-422 and by the National Science Foundation under Grant MCS75-222-55 |
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Keywords: | AMS(MOS): 65F10 CR: 5 14 |
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