A FAST ALGORITHM FOR THE EVALUATION OF LEGENDRE EXPANSIONS

被引：129

作者：

ALPERT, BK

ROKHLIN, V

机构：

[1] YALE UNIV,DEPT MATH,NEW HAVEN,CT 06520

[2] YALE UNIV,DEPT COMP SCI,NEW HAVEN,CT 06520

[3] UNIV CALIF BERKELEY LAWRENCE BERKELEY LAB,BERKELEY,CA 94720

来源：

SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING | 1991年 / 12卷 / 01期

关键词：

FAST TRANSFORM; LEGENDRE SERIES; CHEBYSHEV SERIES; APPROXIMATION THEORY;

D O I：

10.1137/0912009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An algorithm is presented for the rapid calculation of the values and coefficients of finite Legendre series. Given an n-term Legendre expansion, the algorithm produces its values at n Chebyshev nodes on the interval [-1,1] for a cost proportional to n log n. Similarly, given the values of a function f at n Chebyshev nodes, the algorithm produces the n-term Legendre expansion of the polynomial of degree n - 1 that is equal to f at these nodes. The cost of the algorithm is roughly three times that of the Fast Fourier Transform of length n, provided that calculations are performed to single precision accuracy. In double precision, the ratio is approximately 5.5. The method employed admits far-reaching generalizations and is currently being applied to several other problems.

引用

页码：158 / 179

页数：22

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