research
∙
05/05/2023
AAA rational approximation on a continuum
AAA rational approximation has normally been carried out on a discrete s...
share
research
∙
02/14/2023
Are sketch-and-precondition least squares solvers numerically stable?
Sketch-and-precondition techniques are popular for solving large least s...
research
∙
01/28/2023
Convergence and Near-optimal Sampling for Multivariate Function Approximations in Irregular Domains via Vandermonde with Arnoldi
Vandermonde matrices are usually exponentially ill-conditioned and often...
research
∙
12/24/2022
Speeding up Krylov subspace methods for computing f(A)b via randomization
This work is concerned with the computation of the action of a matrix fu...
research
∙
12/02/2022
Randomized low-rank approximation for symmetric indefinite matrices
The Nyström method is a popular choice for finding a low-rank approximat...
research
∙
11/09/2022
Efficient Bounds and Estimates for Canonical Angles in Randomized Subspace Approximations
Randomized subspace approximation with "matrix sketching" is an effectiv...
research
∙
06/02/2022
A Fast Randomized Algorithm for computing the Null Space
Randomized algorithms in numerical linear algebra can be fast, scalable ...
research
∙
03/16/2022
A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices
We devise a spectral divide-and-conquer scheme for matrices that are sel...
research
∙
03/14/2022
Randomized algorithms for Tikhonov regularization in linear least squares
We describe two algorithms to efficiently solve regularized linear least...
research
∙
01/26/2022
Stochastic diagonal estimation: probabilistic bounds and an improved algorithm
We study the problem of estimating the diagonal of an implicitly given m...
research
∙
12/27/2021
Rectangular eigenvalue problems
Often the easiest way to discretize an ordinary or partial differential ...
research
∙
10/29/2021
Fast Accurate Randomized Algorithms for Linear Systems and Eigenvalue Problems
This paper develops a new class of algorithms for general linear systems...
research
∙
10/14/2021
A Theory of Quantum Subspace Diagonalization
Quantum subspace diagonalization methods are an exciting new class of al...
research
∙
09/11/2021
Least-squares spectral methods for ODE eigenvalue problems
We develop spectral methods for ODEs and operator eigenvalue problems th...
research
∙
05/17/2021
Full operator preconditioning and the accuracy of solving linear systems
Unless special conditions apply, the attempt to solve ill-conditioned sy...
research
∙
05/16/2021
Fast randomized numerical rank estimation
Matrices with low-rank structure are ubiquitous in scientific computing....
research
∙
04/14/2021
Stable and Efficient Computation of Generalized Polar Decompositions
We present methods for computing the generalized polar decomposition of ...
research
∙
11/21/2020
Zolotarev's fifth and sixth problems
In an influential 1877 paper, Zolotarev asked and answered four question...
research
∙
10/19/2020
Twice is enough for dangerous eigenvalues
We analyze the stability of a class of eigensolvers that target interior...
research
∙
10/05/2020
Reciprocal-log approximation and planar PDE solvers
This article is about both approximation theory and the numerical soluti...
research
∙
09/23/2020
Fast and stable randomized low-rank matrix approximation
Randomized SVD has become an extremely successful approach for efficient...
research
∙
08/07/2020
Solving two-parameter eigenvalue problems using an alternating method
We present a new approach to compute selected eigenvalues and eigenvecto...
research
∙
07/23/2020
Exponential node clustering at singularities for rational approximation, quadrature, and PDEs
Rational approximations of functions with singularities can converge at ...
research
∙
04/04/2020
Rational neural networks
We consider neural networks with rational activation functions. The choi...
research
∙
11/22/2019
Vandermonde with Arnoldi
Vandermonde matrices are exponentially ill-conditioned, rendering the fa...
research
∙
10/16/2019
Weighted Monte Carlo with least squares and randomized extended Kaczmarz for option pricing
We propose a methodology for computing single and multi-asset European o...
research
∙
08/16/2019
An algorithm for real and complex rational minimax approximation
Rational minimax approximation of real functions on real intervals is an...
research
∙
08/05/2019
Accuracy of approximate projection to the semidefinite cone
When a projection of a symmetric or Hermitian matrix to the positive sem...
research
∙
06/26/2019
Approximating the pth Root by Composite Rational Functions
A landmark result from rational approximation theory states that x^1/p o...
research
∙
07/09/2017