9 papers
Computing accurate singular vectors and eigenvectors using mixed-precision Jacobi algorithms
Zhengbo Zhou, Françoise Tisseur, Marcus Webb
Mixed-precision variants of the Jacobi algorithm for symmetric positive definite eigenproblems and the one-sided Jacobi algorithm for singular value decompositions have recently be…
Low-rank approximation of analytic kernels
Marcus Webb
Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is…
Stable Hermite transforms via the Golub-Welsch algorithm
Marcus Webb, Georg Maierhofer
We introduce an efficient stable algorithm for transforms associated with expansions in Hermite functions interpolated at Hermite polynomial roots. The Hermite transform matrix can…
T-systems: a theory of orthonormal functions with a tridiagonal differentiation matrix
Arieh Iserles, Marcus Webb
The starting point of this paper is that a spectral method is essentially a combination of an orthonormal basis of the underlying Hilbert space with Galerkin conditions. The choice…
Computing accurate singular values using a mixed-precision one-sided Jacobi algorithm
Zhengbo Zhou, Françoise Tisseur, Marcus Webb
We present a relative forward error analysis of a mixed-precision preconditioned one-sided Jacobi algorithm, analogous to a two-sided version introduced in [N. J. Higham, F. Tisseu…
Simulation of Radiation Chemistry by a One-Shot Hybrid Continuum / Monte Carlo Method
Charlie Fynn Perkins, Marcus Webb, Fred J. Currell
Understanding the spatio-temporal evolution of radiolytic species created by high-energy electrons in water underpins key applications from radiotherapy and nuclear safety to envir…