Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On fractional asymptotical regularization of linear ill-posed problems
  in Hilbert spaces   In this paper, we study a fractional-order variant of the asymptotical
regularization method, called {\it Fractional Asymptotical Regularization
(FAR)}, for solving linear ill-posed operator equations in a Hilbert space
setting. We assign the method to the general linear regularization schema and
prove that under certain smoothness assumptions, FAR with fractional order in
the range $(1,2)$ yields an acceleration with respect to comparable order
optimal regularization methods. Based on the one-step Adams-Moulton method, a
novel iterative regularization scheme is developed for the numerical
realization of FAR. Two numerical examples are given to show the accuracy and
the acceleration effect of FAR.

6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin