@TechReport{	  it:2021-005,
  author	= {Giovanni Barbarino and Melker Claesson and Sven-Erik
		  Ekstr{\"o}m and Carlo Garoni and David Meadon},
  title		= {Matrix-Less Eigensolver for Large Structured Matrices},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2021},
  number	= {2021-005},
  month		= aug,
  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 the working hypothesis,
		  which is proved to be plausible through numerical
		  experiments, we propose an eigensolver for the computation
		  of the eigenvalues of $X_n$ for large~$n$. The performance
		  of the eigensolver---which is called matrix-less because it
		  does not operate on the matrix $X_n$---is illustrated on
		  several numerical examples, with a special focus on
		  matrices arising from the discretization of differential
		  problems, and turns out to be quite satisfactory in all
		  cases. In a sense, this is an a posteriori proof of the
		  reasonableness of the working hypothesis as well as a
		  testimony of the fact that the spectra of large structured
		  matrices are much more ``regular'' than one might expect.},
  note		= {Updated 2021-09-03 and 2021-09-08.}
}