Math @ Duke

Publications [#328965] of Yingzhou Li
Papers Published
 Li, Y; Yang, H; Ying, L, Multidimensional butterfly factorization,
Applied and Computational Harmonic Analysis, vol. 44 no. 3
(May, 2018),
pp. 737758, Elsevier BV [doi]
(last updated on 2019/10/16)
Abstract: © 2017 Elsevier Inc. This paper introduces the multidimensional butterfly factorization as a datasparse representation of multidimensional kernel matrices that satisfy the complementary lowrank property. This factorization approximates such a kernel matrix of size N×N with a product of O(logN) sparse matrices, each of which contains O(N) nonzero entries. We also propose efficient algorithms for constructing this factorization when either (i) a fast algorithm for applying the kernel matrix and its adjoint is available or (ii) every entry of the kernel matrix can be evaluated in O(1) operations. For the kernel matrices of multidimensional Fourier integral operators, for which the complementary lowrank property is not satisfied due to a singularity at the origin, we extend this factorization by combining it with either a polar coordinate transformation or a multiscale decomposition of the integration domain to overcome the singularity. Numerical results are provided to demonstrate the efficiency of the proposed algorithms.


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