Fast algorithms for discrete polynomial transforms on arbitrary grids

DOI10.1016/S0024-3795(02)00592-XzbMath1026.65137MaRDI QIDQ1874677

Daniel Potts

Publication date: 25 May 2003

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

algorithmnumerical examplesfast Fourier transformgrids\(B\)-splinesmatrix-vector productfast polynomial transformtransformChebyshev knotsGaussian bellsVandermonde-like matrixdiscrete polynomial transformfast cosinenonequi-spaced

Mathematics Subject Classification ID

Numerical methods for discrete and fast Fourier transforms (65T50)

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Cites Work

• Unnamed Item
• Fast polynomial multiplication and convolutions related to the discrete cosine transform
• The operational properties of the Chebyshev transform. I: General properties
• A note on fast Fourier transforms for nonequispaced grids
• Computing Fourier transforms and convolutions on the 2-sphere
• Fast Fourier transforms for nonequispaced data. II
• On the construction of wavelets on a bounded interval
• On the fast Fourier transform of functions with singularities
• Fast algorithms for discrete polynomial transforms
• Fast Approximate Fourier Transforms for Irregularly Spaced Data
• An Improved Fast Multipole Algorithm for Potential Fields on the Line
• Fast Fourier Transforms for Nonequispaced Data
• Fast Discrete Polynomial Transforms with Applications to Data Analysis for Distance Transitive Graphs
• The Regular Fourier Matrices and Nonuniform Fast Fourier Transforms
• Fast Algorithms for Polynomial Interpolation, Integration, and Differentiation
• A Polynomial Approach to Fast Algorithms for Discrete Fourier-Cosine and Fourier-Sine Transforms