Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial Preconditioned Arnoldi   Polynomial preconditioning can improve the convergence of the Arnoldi method
for computing eigenvalues. Such preconditioning significantly reduces the cost
of orthogonalization; for difficult problems, it can also reduce the number of
matrix-vector products. Parallel computations can particularly benefit from the
reduction of communication-intensive operations. The GMRES algorithm provides a
simple and effective way of generating the preconditioning polynomial. For some
problems high degree polynomials are especially effective, but they can lead to
stability problems that must be mitigated. A two-level "double polynomial
preconditioning" strategy provides an effective way to generate high-degree
preconditioners.

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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th