Fast summation based on fast trigonometric transforms at non‐equispaced nodes | Zendy

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Fast summation based on fast trigonometric transforms at non‐equispaced nodes

Author(s) -

Fenn Markus,

Potts Daniel

Publication year - 2004

Publication title -

numerical linear algebra with applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.02

H-Index - 53

eISSN - 1099-1506

pISSN - 1070-5325

DOI - 10.1002/nla.407

Subject(s) - trigonometry , computation , mathematics , matrix (chemical analysis) , algorithm , combinatorics , discrete mathematics , mathematical analysis , materials science , composite material

We develop a new algorithm for the fast computation of matrix–vector products with special matrices. More precisely we develop a method for the fast computation of sums f ( y j ):= ∑ k =1 Nα k K ( y j − x k ) at non‐equispaced nodes x k and y j ( j =1,…, M ) which requires only ( N log N + ( M + N )) arithmetic operations. Our algorithm is based on a novel approach to fast discrete trigonometric transforms at non‐equispaced nodes. Copyright © 2004 John Wiley & Sons, Ltd.

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