Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Methods for the QCD Overlap Operator:III. Nested Iterations   The numerical and computational aspects of chiral fermions in lattice quantum
chromodynamics are extremely demanding. In the overlap framework, the
computation of the fermion propagator leads to a nested iteration where the
matrix vector multiplications in each step of an outer iteration have to be
accomplished by an inner iteration; the latter approximates the product of the
sign function of the hermitian Wilson fermion matrix with a vector. In this
paper we investigate aspects of this nested paradigm. We examine several Krylov
subspace methods to be used as an outer iteration for both propagator
computations and the Hybrid Monte-Carlo scheme. We establish criteria on the
accuracy of the inner iteration which allow to preserve an a priori given
precision for the overall computation. It will turn out that the accuracy of
the sign function can be relaxed as the outer iteration proceeds. Furthermore,
we consider preconditioning strategies, where the preconditioner is built upon
an inaccurate approximation to the sign function. Relaxation combined with
preconditioning allows for considerable savings in computational efforts up to
a factor of 4 as our numerical experiments illustrate. We also discuss the
possibility of projecting the squared overlap operator into one chiral sector.

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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an