UPDATING AND DOWNDATING OF ORTHOGONAL POLYNOMIALS WITH DATA FITTING APPLICATIONS

被引：30

作者：

ELHAY, S

GOLUB, GH

KAUTSKY, J

机构：

[1] STANFORD UNIV,DEPT COMP SCI,STANFORD,CA 94305

[2] FLINDERS UNIV,SCH MATH SCI,BEDFORD PK,SA 5042,AUSTRALIA

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1991年 / 12卷 / 02期

关键词：

UPDATING; DOWNDATING; LEAST SQUARES; POLYNOMIAL FITS; DISCRETE INNER PRODUCTS; ORTHOGONAL POLYNOMIALS; JACOBI MATRICES;

D O I：

10.1137/0612024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

New methods for updating and downdating least squares polynomial fits to discrete data are derived and assessed using polynomials orthogonal on all the data points being used. Rather than fixing on one basis throughout, the methods adaptively update and downdate both the least squares fit and the polynomial basis. This is achieved by performing similarity transformations on the tridiagonal Jacobi matrices representing the basis. Although downdating is potentially unstable, experimental results show that the methods give satisfactory results for low degree fits. Details of new algorithms implementing the methods are given, the most economical of which needs 14n + O(1) flops and 2n square roots to update a fit of order n.

引用

页码：327 / 353

页数：27