From high oscillation to rapid approximation III: multivariate expansions
From high oscillation to rapid approximation III: multivariate expansions
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从高振荡到快速逼近 III：多元展开
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
S. P. Nørsett
中科院分区：
文献类型：
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作者：
A. Iserles;S. P. Nørsett
In this paper, we expand upon the theme of modified Fourier expansions and extend the theory to a multivariate setting and to expansions in eigenfunctions of the Laplace-Neumann operator. We pay detailed attention to expansions in a d-dimensional cube and to an effective derivation of expansion coefficients there by means of quadratures of highly oscillatory integrals. Thus, we present asymptotic and Filon-type formulae for an effective derivation of expansion coefficients and discuss their design and relative advantages. Such methods are effective only for large indices; hence, we introduce and analyse alternative quadrature schemes that require a relatively modest number of additional function evaluations.
