Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Solvers for Linear Systems with Fractional Powers of Sparse SPD
  Matrices   In this paper we consider efficient algorithms for solving the algebraic
equation ${\mathcal A}^\alpha {\bf u}={\bf f}$, $0< \alpha <1$, where
${\mathcal A}$ is a symmetric and positive definite matrix obtained form finite
difference or finite element approximations of second order elliptic problems
in ${\mathbb R}^d$, $d=1,2,3$. The method is based on the best uniform rational
approximation of the function $t^{\beta-\alpha}$ for $0 < t \le 1$ and natural
$\beta$, and the assumption that one has at hand an efficient method (e.g.
multigrid, multilevel, or other fast algorithm) for solving equations like
$({\mathcal A} +c {\mathcal I}){\bf u}= {\bf f}$, $c \ge 0$. The provided
numerical experiments on model problems with ${\mathcal A}$ obtained by finite
element approximation of elliptic equations in one and three spacial dimensions
confirm the efficiency of the proposed algorithms.

24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys