Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A converse result for Banach space convergence rates in Tikhonov-type
  convex regularization of ill-posed linear equations   We consider Tikhonov-type variational regularization of ill-posed linear
operator equations in Banach spaces with general convex penalty functionals.
Upper bounds for certain error measures expressing the distance between exact
and regularized solutions, especially for Bregman distances, can be obtained
from variational source conditions. We prove that such bounds are optimal in
case of twisted Bregman distances, that is, the rate function is also an
asymptotic lower bound for the error measure. This result extends existing
converse results from Hilbert space settings to Banach spaces without adhering
to spectral theory.

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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: nucl-th