Computing orthogonal polynomials

被引:0
作者
Landram, FG [1 ]
Alidaee, B [1 ]
机构
[1] UNIV MISSISSIPPI,MANAGEMENT & MKT DEPT,MISSISSIPPI STATE,MS 38677
关键词
D O I
10.1016/S0305-0548(96)00071-8
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
A simple transformation for achieving orthogonal polynomials of any order is described in this article. This transformation, called the residual procedure, is easy to understand, easy to implement in existing programs, and applicable for polynomial regression models whose data are unequally spaced. This same procedure is used in obtaining coefficients for orthogonal contrasts in the analysis of variance. The simplicity of this procedure also makes it easily adaptable to spread-sheet and data base applications. (C) 1997 Published by Elsevier Science Ltd. All rights reserved.
引用
收藏
页码:473 / 476
页数:4
相关论文
共 50 条
[41]   USE OF ORTHOGONAL POLYNOMIALS [J].
COOPER, BE .
THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS, 1968, 17 (03) :283-&
[42]   ASYMPTOTICS FOR ORTHOGONAL POLYNOMIALS [J].
Van Assche, W .
LECTURE NOTES IN MATHEMATICS, 1987, 1265 :1-+
[43]   VECTOR ORTHOGONAL POLYNOMIALS [J].
DRAUX, A ;
MAANAOUI, A .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1990, 32 (1-2) :59-68
[44]   ON THE ASSOCIATED ORTHOGONAL POLYNOMIALS [J].
BELMEHDI, S .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1990, 32 (03) :311-319
[45]   Orthogonal homogeneous polynomials [J].
Fryant, A ;
Naftalevich, A ;
Vemuri, MK .
ADVANCES IN APPLIED MATHEMATICS, 1999, 22 (03) :371-379
[46]   Orthogonal polynomials on the disc [J].
Waldron, Shayne .
JOURNAL OF APPROXIMATION THEORY, 2008, 150 (02) :117-131
[47]   Lectures on orthogonal polynomials [J].
Ismail, MEH .
DIFFERENTIAL EQUATIONS & ASYMPTOTIC THEORY MATHEMATICAL PHYSICS, 2004, 2 :1-43
[48]   LACUNARY ORTHOGONAL POLYNOMIALS [J].
VANROSSUM, H .
KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETESCHAPPEN-PROCEEDINGS SERIES A-MATHEMATICAL SCIENCES, 1966, 69 (01) :55-+
[49]   Coherent orthogonal polynomials [J].
Celeghini, E. ;
del Olmo, M. A. .
ANNALS OF PHYSICS, 2013, 335 :78-85
[50]   Orthogonal polynomials and combinatorics [J].
Stanton, D .
SPECIAL FUNCTIONS 2000: CURRENT PERSPECTIVE AND FUTURE DIRECTIONS, 2001, 30 :389-409