Masters Theses

Abstract

“The use of rational polynomials for approximating surfaces is investigated in this study. In particular, methods for estimating parameters for a rational polynomial model were investigated.

A method is presented for finding initial estimates of the parameters. Two iterative methods are discussed for improving those estimates in an attempt to minimize the sum of the squares of the residuals. These two methods are (1) Scarborough’s Method for applying the theory of least squares to nonlinear models and (2) the Method of Steepest Descent.

Data from two functions were chosen and approximated as illustrations. Each set of data was used two ways, (1) as generated, and (2) with random errors added, thus giving four examples.

Scarborough’s Method for improving the starting values was very effective, for the examples chosen, and the approximations were excellent. The study indicates, therefore, that rational polynomials have good potential as useful functions for surface approximants"--Abstract, page ii.

Advisor(s)

Johnson, Charles A.

Committee Member(s)

Miles, Aaron J.
Antle, Charles E.
Govier, John P., 1913-1998

Department(s)

Mathematics and Statistics

Degree Name

M.S. in Applied Mathematics

Publisher

Missouri School of Mines and Metallurgy

Publication Date

1963

Pagination

iv, 28 pages

Note about bibliography

Includes bibliographical references (page 24).

Rights

© 1963 Thomas B. Baird, All rights reserved.

Document Type

Thesis - Open Access

File Type

text

Language

English

Thesis Number

T 1520

Print OCLC #

5954383

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Included in

Mathematics Commons

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