Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Error Estimates for Arnoldo-Tikhonov Regularization for Ill-Posed
  Operator Equations   Most of the literature on the solution of linear ill-posed operator
equations, or their discretization, focuses only on the infinite-dimensional
setting or only on the solution of the algebraic linear system of equations
obtained by discretization. This paper discusses the influence of the
discretization error on the computed solution. We consider the situation when
the discretization used yields an algebraic linear system of equations with a
large matrix. An approximate solution of this system is computed by first
determining a reduced system of fairly small size by carrying out a few steps
of the Arnoldi process. Tikhonov regularization is applied to the reduced
problem and the regularization parameter is determined by the discrepancy
principle. Errors incurred in each step of the solution process are discussed.
Computed examples illustrate the error bounds derived.

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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat