Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudoinverse-free randomized block iterative algorithms for consistent
  and inconsistent linear systems   Randomized iterative algorithms have attracted much attention in recent years
because they can approximately solve large-scale linear systems of equations
without accessing the entire coefficient matrix. In this paper, we propose two
novel pseudoinverse-free randomized block iterative algorithms for solving
consistent and inconsistent linear systems. The proposed algorithms require two
user-defined random matrices: one for row sampling and the other for column
sampling. We can recover the well-known doubly stochastic Gauss--Seidel,
randomized Kaczmarz, randomized coordinate descent, and randomized extended
Kaczmarz algorithms by choosing appropriate random matrices used in our
algorithms. Because our algorithms allow for a much wider selection of these
two random matrices, a number of new specific algorithms can be obtained. We
prove the linear convergence in the mean square sense of our algorithms.
Numerical experiments for linear systems with synthetic and real-world
coefficient matrices demonstrate the efficiency of some special cases of our
algorithms.

5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics