Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed Points of Averages of Resolvents: Geometry and Algorithms   To provide generalized solutions if a given problem admits no actual solution
is an important task in mathematics and the natural sciences. It has a rich
history dating back to the early 19th century when Carl Friedrich Gauss
developed the method of least squares of a system of linear equations - its
solutions can be viewed as fixed points of averaged projections onto
hyperplanes. A powerful generalization of this problem is to find fixed points
of averaged resolvents (i.e., firmly nonexpansive mappings).
  This paper concerns the relationship between the set of fixed points of
averaged resolvents and certain fixed point sets of compositions of resolvents.
It partially extends recent work for two mappings on a question of C. Byrne.
The analysis suggests a reformulation in a product space.
  Furthermore, two new algorithms are presented. A complete convergence proof
that is based on averaged mappings is provided for the first algorithm. The
second algorithm, which currently has no convergence proof, iterates a mapping
that is not even nonexpansive. Numerical experiments indicate the potential of
these algorithms when compared to iterating the average of the resolvents.

6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci