6 papers
Sketch-and-Restart: Randomized Sketching in Quadrature-Based Restarting for Matrix Functions
Stefan Güttel, Jingyu Liu, Lauri Nyman
We develop a sketch-and-restart framework for computing the action of a matrix function on a vector, , where is large, sparse, and non-Hermitian. The framework combines…
Nearest matrix with multiple eigenvalues by Riemannian optimization
Vanni Noferini, Lauri Nyman, Federico Poloni
Given a square complex matrix , we tackle the problem of finding the nearest matrix with multiple eigenvalues or, equivalently when had distinct eigenvalues, the nearest def…
Flexible GMRES converges in two phases
Stefan Güttel, Lauri Nyman
We derive a sharp upper bound on the residuals produced by the flexible GMRES (FGMRES) method. The bound shows that FGMRES exhibits two phases of convergence depending on the resid…
Singular vector spaces for computing the structured distance to singularity
Lauri Nyman
Finding the distance to singularity for a matrix is a ubiquitous problem in numerical linear algebra, and is elegantly solved by the Eckart-Young-Mirsky theorem. Its structured var…
Riemann-Oracle: A general-purpose Riemannian optimizer to solve nearness problems in matrix theory
Miryam Gnazzo, Vanni Noferini, Lauri Nyman +1
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a ma…
Finding the nearest -stable pencil with Riemannian optimization
Vanni Noferini, Lauri Nyman
This paper considers the problem of finding the nearest -stable pencil to a given square pencil , where a pencil is called -stable if it i…