73 citations · 398 across the 44 of their papers we have counts for
6 papers · 1 filter
Vector spaces of linearizations for matrix polynomials: a bivariate polynomial approach
Yuji Nakatsukasa, Vanni Noferini, Alex Townsend
We revisit the landmark paper [D. S. Mackey, N. Mackey, C. Mehl, and V. Mehrmann, SIAM J. Matrix Anal. Appl., 28 (2006), pp.~971--1004] and, by viewing matrices as coefficients for…
On the singular values of matrices with displacement structure
Bernhard Beckermann, Alex Townsend
Matrices with displacement structure such as Pick, Vandermonde, and Hankel matrices appear in a diverse range of applications. In this paper, we use an extremal problem involving r…
Stable extrapolation of analytic functions
Laurent Demanet, Alex Townsend
This paper examines the problem of extrapolation of an analytic function for given perturbed samples from an equally spaced grid on . Mathematical folklore states t…
Fast polynomial transforms based on Toeplitz and Hankel matrices
Alex Townsend, Marcus Webb, Sheehan Olver
Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonally-scaled Hadamard products involving Toeplitz…
Computing with functions in spherical and polar geometries II. The disk
Heather Wilber, Alex Townsend, Grady Wright
A collection of algorithms is described for numerically computing with smooth functions defined on the unit disk. Low rank approximations to functions in polar geometries are forme…
Gaussian elimination corrects pivoting mistakes
Alex Townsend
Gaussian elimination (GE) is the archetypal direct algorithm for solving linear systems of equations and this has been its primary application for thousands of years. In the last d…