3 papers
math.NA2025
Mixed-precision algorithms for solving the Sylvester matrix equation
Andrii Dmytryshyn, Massimiliano Fasi, Nicholas J. Higham +1
We consider the solution of the Sylvester equation in mixed precision. We derive a new iterative refinement scheme to solve perturbed quasi-triangular Sylvester equations…
math.NA2025
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…
math.NA2023
The Power of Bidiagonal Matrices
Nicholas J. Higham
Bidiagonal matrices are widespread in numerical linear algebra, not least because of their use in the standard algorithm for computing the singular value decomposition and their ap…