9 papers · 1 filter
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…
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…