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Least squares orthogonal polynomial approximation in several independent variables

Technical Report:

Abstract

This paper begins with an exposition of a systematic technique for generating orthonormal polynomials in two independent variables by application of the Gram-Schmidt orthogonalization procedure of linear algebra. It is then demonstrated how a linear least squares approximation for experimental data or an arbitrary function can be generated from these polynomials. The least squares coefficients are computed without recourse to matrix arithmetic, which ensures both numerical stability and simplicity of implementation as a self contained numerical algorithm. The Gram-Schmidt procedure is then utilised to generate a complete set of orthogonal polynomials of fourth degree. A theory for the transformation of the polynomial representation from an arbitrary basis into the familiar sum of products form is presented, together with a specific implementation for fourth degree polynomials. Finally, the computational integrity of this algorithm is verified by reconstructing arbitrary fourth degree polynomials from their values at randomly chosen points in their domain. 13 refs., 1 tab.
Authors:
Publication Date:
Jun 01, 1992
Product Type:
Technical Report
Report Number:
ESM-46
Reference Number:
SCA: 661100; PA: AIX-24:003162; SN: 93000913680
Resource Relation:
Other Information: PBD: Jun 1992
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; POLYNOMIALS; ORTHOGONAL TRANSFORMATIONS; ALGORITHMS; MATRICES; NUMERICAL DATA; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10108962
Research Organizations:
Flinders Univ. of South Australia, Adelaide, SA (Australia). Electronic Structure of Materials Centre
Country of Origin:
Australia
Language:
English
Other Identifying Numbers:
Other: ON: DE93609832; TRN: AU9212903003162
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
[29] p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Caprari, R S. Least squares orthogonal polynomial approximation in several independent variables. Australia: N. p., 1992. Web.
Caprari, R S. Least squares orthogonal polynomial approximation in several independent variables. Australia.
Caprari, R S. 1992. "Least squares orthogonal polynomial approximation in several independent variables." Australia.
@misc{etde_10108962,
title = {Least squares orthogonal polynomial approximation in several independent variables}
author = {Caprari, R S}
abstractNote = {This paper begins with an exposition of a systematic technique for generating orthonormal polynomials in two independent variables by application of the Gram-Schmidt orthogonalization procedure of linear algebra. It is then demonstrated how a linear least squares approximation for experimental data or an arbitrary function can be generated from these polynomials. The least squares coefficients are computed without recourse to matrix arithmetic, which ensures both numerical stability and simplicity of implementation as a self contained numerical algorithm. The Gram-Schmidt procedure is then utilised to generate a complete set of orthogonal polynomials of fourth degree. A theory for the transformation of the polynomial representation from an arbitrary basis into the familiar sum of products form is presented, together with a specific implementation for fourth degree polynomials. Finally, the computational integrity of this algorithm is verified by reconstructing arbitrary fourth degree polynomials from their values at randomly chosen points in their domain. 13 refs., 1 tab.}
place = {Australia}
year = {1992}
month = {Jun}
}