@TechReport{ it:2021-007,
author = {Giovanni Barbarino and Melker Claesson and Sven-Erik
Ekstr{\"o}m and Carlo Garoni and David Meadon and Hendrik
Speleers},
title = {Matrix-Less Eigensolver for Large Structured Matrices},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2021},
number = {2021-007},
month = nov,
abstract = {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 $X_n$ 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 $X_n$ 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 $X_n$ 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.}
}