Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to optimize preconditioners for the conjugate gradient method: a
  stochastic approach   The conjugate gradient method (CG) is typically used with a preconditioner
which improves efficiency and robustness of the method. Many preconditioners
include parameters and a proper choice of a preconditioner and its parameters
is often not a trivial task. Although many convergence estimates exist which
can be used for optimizing preconditioners, these estimates typically hold for
all initial guess vectors, in other words, they reflect the worst convergence
rate. To account for the mean convergence rate instead, in this paper, we
follow a stochastic approach. It is based on trial runs with random initial
guess vectors and leads to a functional which can be used to monitor
convergence and to optimize preconditioner parameters in CG. Presented
numerical experiments show that optimization of this new functional with
respect to preconditioner parameters usually yields a better parameter value
than optimization of the functional based on the spectral condition number.

27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs