Application of linear programming techniques to minimax approximation

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Mary Elizabeth Evans (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
D. McAllister

Abstract: A. Interpolation and Approximation The problem with which we are concerned is that of finding some function P(x) which "most closely" approximates a given function F(x). There are two main ways of doing this interpolation and approximation. Here we will consider in detail only the latter—actually only Chebychev approximation. However it will be useful to first ask ourselves when we approximate and especially when we choose to use Chebychev approximation. The interpolation method consists of finding a polynomial which passes exactly through each one of a given set of points. We can get this result by using an interpolating polynomial of degree n-1, where n is the number of given points. This method can be quite accurate and easy to use with a relatively "small" number of points. However, if we try to interpolate 1000 points, we would have to use a 999th degree polynomial, which would be extremely "wiggly."

Additional Information

Honors Project
Language: English
Date: 1969

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