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Mathematics of Computation

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



Detection of singularities using segment approximation

Authors: R. Grothmann and H. N. Mhaskar
Journal: Math. Comp. 59 (1992), 533-540
MSC: Primary 41A15; Secondary 41A10, 65D15
MathSciNet review: 1145662
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Abstract: We discuss best segment approximation (with free knots) by polynomials to piecewise analytic functions on a real interval. It is shown that, if the degree of the polynomials tends to infinity and the number of knots is the same as the number of singularities of the function, then the optimal knots converge geometrically fast to the singularities. When the degree is held fixed and the number of knots tends to infinity, we study the asymptotic distribution of the optimal knots.

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Article copyright: © Copyright 1992 American Mathematical Society