On Polynomial Function Approximation with Minimum Mean Squared Relative Error and a Problem of Tchebychef
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Authors
Borges, Carlos F.
Subjects
Approximation
Relative Error
Relative Error
Advisors
Date of Issue
2015
Date
Publisher
Language
Abstract
We consider the problem of constructing a polynomial approximation to a function f(x) over the interval [--1; 1] that minimizes the mean squared relative error
(MMSRE) over the interval. We establish sufficient conditions for solving the problem. We then consider a classic problem from a paper of Tchebychef and
compare his solution to MMSRE, demonstrating that in some cases the latter approach can yield a more appealing solution and one that it is applicable in a
number of situations where the Tchebychef approach is not.
Type
Article
Description
The article of record as published may be found at: http://dx.doi.org/10.1016/j.amc.2015.01.121
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
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NPS Report Number
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Funding
Format
Citation
C. Borges, "On Polynomial Function Approximation with Minimum Mean Squared Relative Error and a Problem of Tchebychef," Applied Mathematics and Computation, v.258, May 1, 2015, pp. 22-28
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.