Applications of the generalized Fourier transform in numerical linear algebra

DOI10.1007/s10543-005-0030-3zbMath1093.65042OpenAlexW2059524338WikidataQ59567750 ScholiaQ59567750MaRDI QIDQ2490360

Krister Åhlander, Hans Z. Munthe-Kaas

Publication date: 2 May 2006

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-005-0030-3

zbMATH Keywords

numerical examplesdiscrete Fourier transformequivariant matricesdiagonalizationcirculant matricesgeneralized Fourier transformblock group algebrasnoncommutative convolutions

Mathematics Subject Classification ID

Related Items (7)

Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the \(D_4\) symmetry group; interpolation within a squircle. I ⋮ Sparse generalized Fourier transforms ⋮ Groups and Symmetries in Numerical Linear Algebra ⋮ Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform ⋮ A framework for FFT-based homogenization on anisotropic lattices ⋮ Eigenvalues for equivariant matrices ⋮ Topics in structure-preserving discretization

Cites Work

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• Symmetry-based matrix factorization
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• Symmetry, groups, and boundary value problems. A progressive introduction to noncommutative harmonic analysis of partial differential equations in domains with geometrical symmetry
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• An abstract theory for the domain reduction method
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• Exploiting Symmetry in Boundary Element Methods
• Fast Fourier Transforms on Finite Non-Abelian Groups
• Boundary Value Problems with Symmetry and Their Approximation by Finite Elements
• Some Error Estimates for the Numerical Approximation of Surface Integrals
• The efficient computation of Fourier transforms on the symmetric group
• Exploiting partial or complete geometrical symmetry in 3D symmetric Galerkin indirect BEM formulations
• Equivariant Preconditioners for Boundary Element Methods
• Separation of variables and the computation of Fourier transforms on finite groups, I
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