56 citations · 287 across the 58 of their papers we have counts for
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GPU Optimizations for the Hierarchical Poincaré-Steklov Scheme
Anna Yesypenko, Per-Gunnar Martinsson
This manuscript presents GPU optimizations for the 2D Hierarchical Poincaré-Steklov (HPS) discretization scheme. HPS is a multi-domain spectral collocation method that combines hig…
SlabLU: A Two-Level Sparse Direct Solver for Elliptic PDEs
Anna Yesypenko, Per-Gunnar Martinsson
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domai…
Efficient Bounds and Estimates for Canonical Angles in Randomized Subspace Approximations
Yijun Dong, Per-Gunnar Martinsson, Yuji Nakatsukasa
Randomized subspace approximation with "matrix sketching" is an effective approach for constructing approximate partial singular value decompositions (SVDs) of large matrices. The…
A Unified Trapezoidal Quadrature Method for Singular and Hypersingular Boundary Integral Operators on Curved Surfaces
Bowei Wu, Per-Gunnar Martinsson
This paper describes a trapezoidal quadrature method for the discretization of singular and hypersingular boundary integral operators (BIOs) that arise in solving boundary value pr…
Solving Linear Systems on a GPU with Hierarchically Off-Diagonal Low-Rank Approximations
Chao Chen, Per-Gunnar Martinsson
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathemat…
Randomized Compression of Rank-Structured Matrices Accelerated with Graph Coloring
James Levitt, Per-Gunnar Martinsson
A randomized algorithm for computing a data sparse representation of a given rank structured matrix (a.k.a. an -matrix) is presented. The algorithm draws on the randomized s…