Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toward a new fully algebraic preconditioner for symmetric positive
  definite problems   A new domain decomposition preconditioner is introduced for efficiently
solving linear systems Ax = b with a symmetric positive definite matrix A. The
particularity of the new preconditioner is that it is not necessary to have
access to the so-called Neumann matrices (i.e.: the matrices that result from
assembling the variational problem underlying A restricted to each subdomain).
All the components in the preconditioner can be computed with the knowledge
only of A (and this is the meaning given here to the word algebraic). The new
preconditioner relies on the GenEO coarse space for a matrix that is a low-rank
modification of A and on the Woodbury matrix identity. The idea underlying the
new preconditioner is introduced here for the first time with a first version
of the preconditioner. Some numerical illustrations are presented. A more
extensive presentation including some improved variants of the new
preconditioner can be found in [7]
(https://hal.archives-ouvertes.fr/hal-03258644).

22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an