Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational spectral filters with optimal convergence rate   In recent years, contour-based eigensolvers have emerged as a standard
approach for the solution of large and sparse eigenvalue problems. Building
upon recent performance improvements through non-linear least square
optimization of so-called rational filters, we introduce a systematic method to
design these filters by minimizing the worst-case convergence ratio and
eliminate the parametric dependence on weight functions. Further, we provide an
efficient way to deal with the box-constraints which play a central role for
the use of iterative linear solvers in contour-based eigensolvers. Indeed,
these parameter-free filters consistently minimize the number of iterations and
the number of FLOPs to reach convergence in the eigensolver. As a byproduct,
our rational filters allow for a simple solution to load balancing when the
solution of an interior eigenproblem is approached by the slicing of the sought
after spectral interval.

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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex