Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Accelerated Coordinate Descent Methods and Faster Algorithms
  for Solving Linear Systems   In this paper we show how to accelerate randomized coordinate descent methods
and achieve faster convergence rates without paying per-iteration costs in
asymptotic running time. In particular, we show how to generalize and
efficiently implement a method proposed by Nesterov, giving faster asymptotic
running times for various algorithms that use standard coordinate descent as a
black box. In addition to providing a proof of convergence for this new general
method, we show that it is numerically stable, efficiently implementable, and
in certain regimes, asymptotically optimal.
  To highlight the computational power of this algorithm, we show how it can
used to create faster linear system solvers in several regimes:
  - We show how this method achieves a faster asymptotic runtime than conjugate
gradient for solving a broad class of symmetric positive definite systems of
equations.
  - We improve the best known asymptotic convergence guarantees for Kaczmarz
methods, a popular technique for image reconstruction and solving
overdetermined systems of equations, by accelerating a randomized algorithm of
Strohmer and Vershynin.
  - We achieve the best known running time for solving Symmetric Diagonally
Dominant (SDD) system of equations in the unit-cost RAM model, obtaining an O(m
log^{3/2} n (log log n)^{1/2} log (log n / eps)) asymptotic running time by
accelerating a recent solver by Kelner et al.
  Beyond the independent interest of these solvers, we believe they highlight
the versatility of the approach of this paper and we hope that they will open
the door for further algorithmic improvements in the future.

22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph