An error analysis for absolute and relative approximation |
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Authors: | A Bacopoulos R V M Zahar |
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Institution: | (1) Département d'Informatique, Université de Montréal, Montréal, Quebec, Canada |
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Abstract: | We consider the vectorial algorithm for finding best polynomial approximationsp P
n
to a given functionf Ca, b], with respect to the norm ·
s
, defined byp – f
s
=w
1 (p – f)+w
2 (p – f) A bound for the modulus of continuity of the best vectorial approximation operator is given, and using the floating point calculus of J. H. Wilkinson, a bound for the rounding error in the algorithm is derived. For givenf, these estimates provide an indication of the conditioning of the problem, an estimate of the obtainable accuracy, and a practical method for terminating the iteration.This paper was supported in part by the Canadian NCR A-8108, FCAC 74-09 and G.E.T.M.A.Part of this research was done during the first-named author's visit to theB! Chair of Applied Mathematics, University of Athens, Spring term, 1975. |
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Keywords: | Primary 41X04 41A05 41A10 41A50 65D15 65G05 Secondary 26A18 26A75 47H15 |
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