This paper consists of two main sections. In the first the bounds are derived for the rounding errors made in the fundamental floating-point arithmetic operations. In the second, these results are applied in the analysis of a number of computing techniques for the calculation of the eigenvalues of matrices. In each case thecomputed solution is expressed as the exact solution of a perturbed version of the original matrix and bounds are found for the perturbations. For one of the techniques, an a priori bound is derived for the errors in the eigenvalues themselves.
KeywordsExact Solution Mathematical Method Error Analysis Arithmetic Operation Computing Technique
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