The Exponentially Convergent Trapezoidal Rule

被引：370

作者：

Trefethen, Lloyd N. ^{[1
]}

Weideman, J. A. C. ^{[2
]}

机构：

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

[2] Univ Stellenbosch, Dept Math Sci, ZA-7602 Matieland, South Africa

来源：

SIAM REVIEW | 2014年 / 56卷 / 03期

基金：

欧洲研究理事会;

关键词：

trapezoidal rule; aliasing; quadrature; resolvent; Hankel contour; double exponential quadrature; FFT; Euler Maclaurin formula; CLENSHAW-CURTIS QUADRATURE; NUMERICAL INVERSION; TIME DISCRETIZATION; LAPLACE TRANSFORMATION; DIFFERENTIAL-EQUATIONS; PERIODIC-FUNCTIONS; SOLVING EVOLUTION; MATRIX FUNCTIONS; FOURIER METHODS; GAUSS-LEGENDRE;

D O I：

10.1137/130932132

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed, and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators.

引用

页码：385 / 458

页数：74

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[3]

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