1 citations · 1 across the 10 of their papers we have counts for
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Sketching Outside the Hilbert Space for the Infinite-Dimensional Randomised SVD
Morgan Lynch-Davies, Marcus Webb
In randomised numerical linear algebra, common choices for distributions of sketch vectors are isotropic, so that . Unfortunately, the natur…
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…
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…
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…
A Riemannian Gradient Descent Method for the Least Squares Inverse Eigenvalue Problem
Alban Bloor Riley, Marcus Webb, Michael L. Baker
We address an algorithm for the least squares fitting of a subset of the eigenvalues of an unknown Hermitian matrix lying an an affine subspace, called the Lift and Projection (LP)…
Computing accurate eigenvalues using a mixed-precision Jacobi algorithm
Nicholas J. Higham, Françoise Tisseur, Marcus Webb +1
We provide a rounding error analysis of a mixed-precision preconditioned Jacobi algorithm, which uses low precision to compute the preconditioner, applies it at high precision (amo…
Deflation Techniques for Finding Multiple Local Minima of a Nonlinear Least Squares Problem
Alban Bloor Riley, Marcus Webb, Michael L Baker
In this paper we generalize the technique of deflation to define two new methods to systematically find many local minima of a nonlinear least squares problem. The methods are base…
A Sherman--Morrison--Woodbury approach to solving least squares problems with low-rank updates
Stefan Güttel, Yuji Nakatsukasa, Marcus Webb +1
We present a simple formula to update the pseudoinverse of a full-rank rectangular matrix that undergoes a low-rank modification, and demonstrate its utility for solving least squa…