@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.}
}