Technical Report 2021-007

Matrix-Less Eigensolver for Large Structured Matrices

Giovanni Barbarino, Melker Claesson, Sven-Erik Ekström, Carlo Garoni, David Meadon, and Hendrik Speleers

November 2021

Sequences of structured matrices of increasing size arise in many scientific applications and especially in the numerical discretization of linear differential problems. We assume as a working hypothesis that the eigenvalues of a matrix Xn belonging to a sequence of this kind are given by a regular expansion. Based on this working hypothesis, which is illustrated to be plausible through numerical experiments, we propose an eigensolver for the computation of the eigenvalues of Xn for large n and we provide a theoretical analysis of its convergence. The eigensolver is called matrix-less because it does not operate on the matrix Xn but on a few similar matrices of smaller size combined with an interpolation-extrapolation strategy. Its performance is benchmarked on several numerical examples, with a special focus on matrices arising from the discretization of differential problems.

Note: Updated version of nr 2021-005.

Available as PDF (12.5 MB, no cover)

Download BibTeX entry.