Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local convergence analysis of the Gauss-Newton-Kurchatov method   We present a local convergence analysis of the Gauss-Newton-Kurchatov method
for solving nonlinear least squares problems with a decomposition of the
operator. The method uses the sum of the derivative of the differentiable part
of the operator and the divided difference of the nondifferentiable part
instead of computing the full Jacobian. A theorem, which establishes the
conditions of convergence, radius and the convergence order of the proposed
method, is proved (Shakhno 2017). However, the radius of convergence is small
in general limiting the choice of initial points. Using tighter estimates on
the distances, under weaker hypotheses (Argyros et al. 2013), we provide an
analysis of the Gauss-Newton-Kurchatov method with the following advantages
over the corresponding results (Shakhno 2017): extended convergence region;
finer error distances, and an at least as precise information on the location
of the solution. The numerical examples illustrate the theoretical results.

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The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
17
The categories of this paper are: q-fin