Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimates for generalized sparse grid hierarchical basis preconditioners   We reconsider some estimates the paper "M. Griebel, P. Oswald, On additive
Schwarz preconditioners for sparse grid discretizations. Numer. Math. 66
(1994), 449-463" concerning the hierarchical basis preconditioner for sparse
grid discretizations. The improvement is in three directions: We consider
arbitrary space dimensions d>1, give bounds for generalized sparse grid spaces
with arbitrary monotone index set, and show that the bounds are sharp up to
constants depending only on d, at least for a subclass of generalized sparse
grid spaces containing full grid, standard sparse grid spaces, and energy-norm
optimized sparse grid spaces.

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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph