AN EXTENSION OF CHEBFUN TO TWO DIMENSIONS

被引：76

作者：

Townsend, Alex ^{[1
]}

Trefethen, Lloyd N. ^{[1
]}

机构：

[1] Univ Oxford, Inst Math, Oxford OX2 6GG, England

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2013年 / 35卷 / 06期

基金：

英国工程与自然科学研究理事会; 欧洲研究理事会;

关键词：

MATLAB; Chebfun; Chebyshev polynomials; low rank approximation; RANK; APPROXIMATION; ALGORITHMS; EQUATIONS;

D O I：

10.1137/130908002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An object-oriented MATLAB system is described that extends the capabilities of Chebfun to smooth functions of two variables defined on rectangles. Functions are approximated to essentially machine precision by using iterative Gaussian elimination with complete pivoting to form "chebfun2" objects representing low rank approximations. Operations such as integration, differentiation, function evaluation, and transforms are particularly efficient. Global optimization, the singular value decomposition, and rootfinding are also extended to chebfun2 objects. Numerical applications are presented.

引用

页码：C495 / C518

页数：24

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