Iterative refinement implies numerical stability |
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Authors: | M Jankowski H Wo?niakowski |
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Institution: | (1) Department of Mathematics, University of Warsaw, 00-901 Warsaw, Poland |
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Abstract: | Suppose that a method computes an approximation of the exact solution of a linear systemAx=b with the relative errorq,q<1. We prove that if all computations are performed in floating point arithmeticfl and single precision, then with iterative refinement is numerically stable and well-behaved wheneverq A A
–1 is at most of order unity. |
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