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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Piecewise monotone interpolation and approximation with Muntz polynomials


Authors: Eli Passow, Louis Raymon and Oved Shisha
Journal: Trans. Amer. Math. Soc. 218 (1976), 197-205
MSC: Primary 41A05
DOI: https://doi.org/10.1090/S0002-9947-1976-0399705-1
MathSciNet review: 0399705
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Abstract: The possibility (subject to certain restrictions) of solving the following approximation and interpolation problem with a given set of ``Muntz polynomials'' on a real interval is demonstrated:

(i) approximation of a continuous function by a ``copositive'' Muntz polynomial;

(ii) approximation of a continuous function by a ``comonotone'' Muntz polynomial;

(iii) approximation of a continuous function with a monotone kth difference by a Muntz polynomial with a monotone kth derivative;

(iv) interpolation by piecewise monotone Muntz polynomials--i. e., polynomials that are monotone on each of the intervals determined by the points of interpolation.

The strong interrelationship of these problems is shown implicitly in the proofs.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0399705-1
Keywords: Approximation, interpolation, Muntz polynomials, restricted approximation, restricted interpolation, monotone approximation, piecewise monotone interpolation
Article copyright: © Copyright 1976 American Mathematical Society