Publications

My work on mixed-precision Jacobi algorithms, with links to papers, accompanying code, and related blog posts.

Preprints

  1. Computing Accurate Singular Vectors and Eigenvectors using Mixed-Precision Jacobi Algorithms

    With Françoise Tisseur and Marcus Webb. arXiv:2606.28069. Jun. 2026.

    Extends the analysis from values to vectors, relating their accuracy to relative spectral gaps and the conditioning of the preconditioned matrix.

    arXiv Code

  2. Computing Accurate Singular Values using a Mixed-Precision One-sided Jacobi Algorithm

    With Françoise Tisseur and Marcus Webb. arXiv:2602.18134. Feb. 2026.

    Uses low-precision preconditioning and a high-precision matrix product to improve singular value accuracy.

    arXiv Code Blog post

Peer-reviewed publications

  1. Computing Accurate Eigenvalues using a Mixed-Precision Jacobi Algorithm

    With Nicholas J. Higham, Françoise Tisseur and Marcus Webb. SIAM J. Matrix Anal. Appl., 46:4. Oct. 2025.

    Combines low-precision preconditioning with Jacobi iteration to improve eigenvalue accuracy for ill-conditioned positive definite matrices.

    arXiv DOI Code Julia package Blog post

Theses

  1. A Mixed Precision Eigensolver Based on the Jacobi Algorithm

    M.Sc. Applied Mathematics, University of Manchester. Sep. 2022.

    arXiv