Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Randomized matrix-free quadrature for spectrum and spectral sum
  approximation   We study randomized matrix-free quadrature algorithms for spectrum and
spectral sum approximation. The algorithms studied are characterized by the use
of a Krylov subspace method to approximate independent and identically
distributed samples of $\mathbf{v}^{\sf H}f[\mathbf{A}]\mathbf{v}$, where
$\mathbf{v}$ is an isotropic random vector, $\mathbf{A}$ is a Hermitian matrix,
and $f[\mathbf{A}]$ is a matrix function. This class of algorithms includes the
kernel polynomial method and stochastic Lanczos quadrature, two widely used
methods for approximating spectra and spectral sums. Our analysis, discussion,
and numerical examples provide a unified framework for understanding randomized
matrix-free quadrature and shed light on the commonalities and tradeoffs
between them. Moreover, this framework provides new insights into the practical
implementation and use of these algorithms, particularly with regards to
parameter selection in the kernel polynomial method.

16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph