14 papers
Accelerating a restarted Krylov method for matrix functions with randomization
Nicolas L. Guidotti, Per-Gunnar Martinsson, Juan A. Acebrón +1
Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subsp…
A stable and fast method for solving multibody scattering problems via the method of fundamental solutions
Yunhui Cai, Joar Bagge, Per-Gunnar Martinsson
The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the…
A time-frequency method for acoustic scattering with trapping
Heather Wilber, Wietse Vaes, Abinand Gopal +1
A Fourier transform method is introduced for a class of hybrid time-frequency methods that solve the acoustic scattering problem in regimes where the solution exhibits both highly…
Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions
Katherine J. Pearce, Per-Gunnar Martinsson
This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algori…
Randomized Block Low-Rank Matrix Compression by Tagging
Katherine J. Pearce, Anna Yesypenko, James Levitt +1
In this work, we present randomized compression algorithms for flat rank-structured matrices with shared bases, termed uniform Block Low-Rank (BLR) matrices. Our main contribution…
Randomized Strong Recursive Skeletonization: Simultaneous Compression and LU Factorization of Hierarchical Matrices using Matrix-Vector Products
Anna Yesypenko, Per-Gunnar Martinsson
The hierarchical matrix framework partitions matrices into subblocks that are either small or of low numerical rank, enabling linear storage complexity and efficient matrix-vector…