Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Algorithms for Positive Semi-Definite Total Least Squares
  Problems, Minimum Rank Problem and Correlation Matrix Computation   We have recently presented a method to solve an overdetermined linear system
of equations with multiple right hand side vectors, where the unknown matrix is
to be symmetric and positive definite. The coefficient and the right hand side
matrices are respectively named data and target matrices. A more complicated
problem is encountered when the unknown matrix is to be positive semi-definite.
The problem arises in estimating the compliance matrix to model deformable
structures and approximating correlation and covariance matrices in financial
modeling. Several methods have been proposed for solving such problems assuming
that the data matrix is unrealistically error free. Here, considering error in
measured data and target matrices, we propose a new approach to solve a
positive semi-definite constrained total least squares problem. We first
consider solving the problem when the rank of the unknown matrix is known, by
defining a new error formulation for the positive semi-definite total least
squares problem and use of optimization methods on Stiefel manifolds. We prove
quadratic convergence of our proposed approach. We then describe how to
generalize our proposed method to solve the general positive semi-definite
total least squares problem. We further apply the proposed approach to solve
the minimum rank problem and the problem of computing correlation matrix.
Comparative numerical results show the efficiency of our proposed algorithms.
Finally, the Dolan-More performance profiles are shown to summarize our
comparative study.

15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn