High dimensional polynomial interpolation on sparse grids

被引：456

作者：

Barthelmann, V

Novak, E

Ritter, K

机构：

[1] 3SOFT, D-91058 Erlangen, Germany

[2] Univ Erlangen Nurnberg, Math Inst, D-91054 Erlangen, Germany

[3] Univ Passau, Fak Math & Informat, D-94030 Passau, Germany

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2000年 / 12卷 / 04期

关键词：

multivariate polynomial interpolation; sparse grids; least solution; universal method; tractability;

D O I：

10.1023/A:1018977404843

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study polynomial interpolation on a d-dimensional cube, where d is large. We suggest to use the least solution at sparse grids with the extrema of the Chebyshev polynomials. The polynomial exactness of this method is almost optimal. Our error bounds show that the method is universal, i.e., almost optimal for many different function spaces. We report on numerical experiments for d=10 using up to 652065 interpolation points.

引用

页码：273 / 288

页数：16

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