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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.