Accurate bidiagonal decomposition of collocation matrices of weighted φ-transformed systems

被引：9

作者：

Mainar, Esmeralda ^{[1
]}

Manuel Pena, Juan ^{[1
]}

Rubio, Beatriz ^{[1
]}

机构：

[1] Univ Zaragoza, Dept Matemat Aplicada, IUMA, Zaragoza, Spain

来源：

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2020年 / 27卷 / 03期

关键词：

accurate computations; bidiagonal decompositions; rational basis; COMPUTATIONS; ALGORITHMS; CURVES;

D O I：

10.1002/nla.2295

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a system of functions, we introduce the concept of weighted phi-transformed system, which will include a very large class of useful representations in Statistics and Computer Aided Geometric Design. An accurate bidiagonal decomposition of the collocation matrices of these systems is obtained. This decomposition is used to present computational methods with high relative accuracy for solving algebraic problems with collocation matrices of weighted phi-transformed systems such as the computation of eigenvalues, singular values, and the solution of some linear systems. Numerical examples illustrate the accuracy of the performed computations.

引用

页数：16

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