Learn More
Kernel matrices are popular in machine learning and scientific computing, but they are limited by their quadratic complexity in both construction and storage. It is well-known that as one varies the kernel parameter, e.g., the width parameter in radial basis function kernels, the kernel matrix changes from a smooth low-rank kernel to a diagonally-dominant(More)
This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) = R d a(x, ξ)e 2πıΦ(x,ξ) f (ξ)dξ, where Φ(x, ξ) is a phase function, a(x, ξ) is an amplitude function, and f (x) is a given input. The frequency domain is hierarchically decomposed into a union of Cartesian coronas. The(More)
The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if either fast algorithms for applying the matrix and its adjoint are available or the entries of the matrix can be sampled individually. For an N × N matrix, the(More)
This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of these transforms satisfy a complementary low-rank property. A preliminary interpolative butterfly factorization is(More)
This paper proposes an efficient method for computing selected generalized eigenpairs of a sparse Hermitian definite matrix pencil (A, B). Based on Zolotarev's best rational function approximations of the signum function and conformal maps, we construct the best rational function approximation of a rectangular function supported on an arbitrary interval.(More)
Low-rank approximations are popular techniques to reduce the high computational cost of large-scale kernel matrices, which are of significant interest in many applications. The success of low-rank methods hinges on the matrix rank, and in practice, these methods are effective even for high-dimensional datasets. The practical success has elicited the(More)
Five phosphorescent metal-anion radical coordination polymers based on a new anion radical ligand generated by in situ deprotonation of a stable zwitterionic radical are described. The N,O,N-tripodal anion radical ligand links metal cations, which leads to five isostructural coordination polymers, [M(3)(bipo(-.))(4)(L)(2)](n) (M=Cd or Mn,(More)
  • 1