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This paper introduces the multidimensional butterfly factorization as a data-sparse representation of multidimensional kernel matrices that satisfy the complementary low-rank property.
Fourier integral operators. I
L. Hörmander · 1971
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A multilevel matrix decomposition algorithm for analyzing scattering from large structures
E. Michielssen and A. Boag · 1996
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Fast computation of Fourier integral operators
E. Candès, L. Demanet, and L. Ying · 2007
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Randomized algorithms for the low-rank approximation of matrices
E. Liberty, F. Woolfe, P.-G. Martinsson, V. Rokhlin, and M. Tygert · 2007
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A fast randomized algorithm for the approximation of matrices
F. Woolfe, E. Liberty, V. Rokhlin, and M. Tygert · 2008
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A fast butterfly algorithm for the computation of Fourier integral operators
E. Candès, L. Demanet, and L. Ying · 2009
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A fast directional algorithm for high frequency acoustic scattering in two dimensions
B. Engquist and L. Ying · 2009
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Sparse Fourier transform via butterfly algorithm
L. Ying · 2009
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An algorithm for the rapid evaluation of special function transforms
M. O’Neil, F. Woolfe, and V. Rokhlin · 2010
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Fast algorithms for spherical harmonic expansions, III
M. Tygert · 2010
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Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions
N. Halko, P. G. Martinsson, and J. A. Tropp · 2011
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Fast construction of hierarchical matrix representation from matrix-vector multiplication
L. Lin, J. Lu, and L. Ying · 2011
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A fast randomized algorithm for computing a hierarchically semiseparable representation of a matrix
P. G. Martinsson · 2011
Wavemoth-fast spherical harmonic transforms by butterfly matrix compression
D. S. Seljebotn · 2012
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A fast algorithm for multilinear operators
H. Yang and L. Ying · 2012
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A fast butterfly algorithm for generalized Radon transforms
J. Hu, S. Fomel, L. Demanet, and L. Ying · 2013
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A parallel butterfly algorithm
J. Poulson, L. Demanet, N. Maxwell, and L. Ying · 2014
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Butterfly Factorization
Y. Li, H. Yang, E. Martin, K. Ho, and L. Ying · 2015
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A multiscale butterfly algorithm for multidimensional Fourier integral operators
Y. Li, H. Yang, and L. Ying · 2015
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Cited alongside, same era.