Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A data scalable augmented Lagrangian KKT preconditioner for large scale
  inverse problems   Current state of the art preconditioners for the reduced Hessian and the
Karush-Kuhn-Tucker (KKT) operator for large scale inverse problems are
typically based on approximating the reduced Hessian with the regularization
operator. However, the quality of this approximation degrades with increasingly
informative observations or data. Thus the best case scenario from a scientific
standpoint (fully informative data) is the worse case scenario from a
computational perspective. In this paper we present an augmented
Lagrangian-type preconditioner based on a block diagonal approximation of the
augmented upper left block of the KKT operator. The preconditioner requires
solvers for two linear subproblems that arise in the augmented KKT operator,
which we expect to be much easier to precondition than the reduced Hessian.
Analysis of the spectrum of the preconditioned KKT operator indicates that the
preconditioner is effective when the regularization is chosen appropriately. In
particular, it is effective when the regularization does not over-penalize
highly informed parameter modes and does not under-penalize uninformed modes.
Finally, we present a numerical study for a large data/low noise Poisson source
inversion problem, demonstrating the effectiveness of the preconditioner. In
this example, three MINRES iterations on the KKT system with our preconditioner
results in a reconstruction with better accuracy than 50 iterations of CG on
the reduced Hessian system with regularization preconditioning.

13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin