Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: GMRES convergence bounds for eigenvalue problems   The convergence of GMRES for solving linear systems can be influenced heavily
by the structure of the right hand side. Within the solution of eigenvalue
problems via inverse iteration or subspace iteration, the right hand side is
generally related to an approximate invariant subspace of the linear system. We
give detailed and new bounds on (block) GMRES that take the special behavior of
the right hand side into account and explain the initial sharp decrease of the
GMRES residual. The bounds give rise to adapted preconditioners applied to the
eigenvalue problems, e.g. tuned and polynomial preconditioners. The numerical
results show that the new (block) GMRES bounds are much sharper than
conventional bounds and that preconditioned subspace iteration with either a
tuned or polynomial preconditioner should be used in practice.

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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics