Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matrix probing and its conditioning   When a matrix A with n columns is known to be well approximated by a linear
combination of basis matrices B_1,..., B_p, we can apply A to a random vector
and solve a linear system to recover this linear combination. The same
technique can be used to recover an approximation to A^-1. A basic question is
whether this linear system is invertible and well-conditioned. In this paper,
we show that if the Gram matrix of the B_j's is sufficiently well-conditioned
and each B_j has a high numerical rank, then n {proportional} p log^2 n will
ensure that the linear system is well-conditioned with high probability. Our
main application is probing linear operators with smooth pseudodifferential
symbols such as the wave equation Hessian in seismic imaging. We demonstrate
numerically that matrix probing can also produce good preconditioners for
inverting elliptic operators in variable media.

28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th