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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Generalized rational Chebyshev approximation

Author: Ichizo Ninomiya
Journal: Math. Comp. 24 (1970), 159-169
MSC: Primary 41.17; Secondary 65.00
MathSciNet review: 0261229
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Abstract: In this paper, a generalized rational Chebyshev approximation problem is considered. The problem is this: To minimize the maximum absolute value of the "criterion function" of the error. By imposing a rather natural restriction on the criterion function, the problem is solved completely; the existence, the uniqueness and the characterization of the best approximation are clarified and interesting relationships between the best approximations corresponding to different criterion functions are found. The theory is applied to the starting rational approximation for Newton iteration for ${x^{1/n}}$.

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Keywords: Rational approximation, criterion function, weight function, best approximation, existence of best approximation, uniqueness of best approximation, characterization of best approximation, relations between best approximations, starting approximation for square root
Article copyright: © Copyright 1970 American Mathematical Society