ISSN:
0945-3245
Keywords:
AMS(MOS): 65F10
;
CR: 5.14
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 α with relative error of order ζ ‖A‖·‖A −1‖ where ζ is the relative computer precision. However with the exception of Gauss-Seidel iteration the residual vector ‖Ax k −b‖ is of order ζ ‖A‖2 ‖A −1‖ ‖α‖ and hence the remaining three iterations arenot well-behaved.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01411845
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