Rational L(2)-approximation with interpolation

Ja-Chen Lin, Purdue University

Abstract

In this thesis we combine L$\sp2$-approximation with interpolation, the approximating functions being chosen to be either polynomials or rational functions with prescribed denominators. Numerical algorithms to achieve this type of approximation are given, and results obtained with a computer are presented to illustrate some of the advantages of constrained L $\sp2$-approximation. We also give detailed analysis of the error of approximation, both in the L$\sp2$-Norm and the Sup-Norm. These formulas for the error can be used to decide whether a given function should be approximated by traditional or constrained L$\sp2$-approximation. We then discuss the problem of rational L$\sp2$-approximation where the denominators are optimized instead of being fixed. Finally, special cases and extensions of our approximation methods are considered.

Degree

Ph.D.

Advisors

Gautschi, Purdue University.

Subject Area

Mathematics

COinS