Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Majorization-type cluster robust bounds for block filters and
  eigensolvers   Convergence analysis of block iterative solvers for Hermitian eigenvalue
problems and the closely related research on properties of matrix-based signal
filters are challenging, and attract increasing attention due to their recent
applications in spectral data clustering and graph-based signal processing. We
combine majorization-based techniques pioneered for investigating the
Rayleigh-Ritz method in [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 1521-1537]
with tools of classical analysis of the block power method by Rutishauser
[Numer. Math., 13 (1969), pp. 4-13] to derive convergence rate bounds of an
abstract block iteration, wherein tuples of tangents of principal angles or
relative errors of Ritz values are bounded using majorization in terms of
arranged partial sums and tuples of convergence factors. Our novel bounds are
robust in presence of clusters of eigenvalues, improve some previous results,
and are applicable to most known block iterative solvers and matrix-based
filters, e.g., to block power, Chebyshev, and Lanczos methods combined with
shift-and-invert approaches and polynomial filtering.

15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom