Error bounds for the integration of singular functions using equidistributed sequences

被引：6

作者：

de Doncker, E ^{[1
]}

Guan, YQ

机构：

[1] Western Michigan Univ, Dept Comp Sci, Kalamazoo, MI 49008 USA

[2] Univ Texas, Dept Comp Sci, Austin, TX 78712 USA

来源：

JOURNAL OF COMPLEXITY | 2003年 / 19卷 / 03期

关键词：

equidistributed point sequence; singularity; asymptotic error terms; extrapolation;

D O I：

10.1016/S0885-064X(03)00029-3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider integral approximations using equidistributed point sequences, which converge for Riemann integrable functions. Under certain conditions, Sobol (Soviet Math. Dokl. 14 (1973) 734) and Klinger (Computing 59 (1997) 223) showed convergence for some classes of singular functions. We focus on asymptotic error bounds and give a scheme for extensions of Sobol's results, thereby obtaining insight in the asymptotic error structure. Numerical examples are presented, validating the principle of "ignoring the singularity" and illustrating the use of extrapolation. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：259 / 271

页数：13

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