18 citations · 41 across the 15 of their papers we have counts for
11 papers · 1 filter
Compression Properties for large Toeplitz-like matrices
Bernhard Beckermann, Daniel Kressner, Heather Wilber
Toeplitz matrices are abundant in computational mathematics, and there is a rich literature on the development of fast and superfast algorithms for solving linear systems involving…
On the rational approximation of Markov functions,with applications to the computation of Markovfunctions of Toeplitz matrices
Bernhard Beckermann, Joanna Bisch, Robert Luce
We investigate the problem of approximating the matrix function by , with a Markov function, a rational interpolant of , and a symmetric Toeplitz matrix…
Low-rank updates of matrix functions II: Rational Krylov methods
Bernhard Beckermann, Alice Cortinovis, Daniel Kressner +1
This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this c…
On the sharpness of the weighted Bernstein-Walsh inequality, with applications to the superlinear convergence of conjugate gradients
Bernhard Beckermann, Thomas Helart
In this paper we show that the weighted Bernstein-Walsh inequality in logarithmic potential theory is sharp up to some new universal constant, provided that the external field is g…
Low-rank updates of matrix functions
Bernhard Beckermann, Daniel Kressner, Marcel Schweitzer
We consider the task of updating a matrix function when the matrix is subject to a low-rank modification. In other words, we aim at approximat…
Rational minimax approximation via adaptive barycentric representations
Silviu-Ioan Filip, Yuji Nakatsukasa, Lloyd N. Trefethen +1
Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation - precisely the case where rational function…