Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Minimum-Rank Gram Matrix Completion via Modified Fixed Point
  Continuation Method   The problem of computing a representation for a real polynomial as a sum of
minimum number of squares of polynomials can be casted as finding a symmetric
positive semidefinite real matrix (Gram matrix) of minimum rank subject to
linear equality constraints.
  In this paper, we propose algorithms for solving the minimum-rank Gram matrix
completion problem, and show the convergence of these algorithms. Our methods
are based on the modified fixed point continuation (FPC) method. We also use
the Barzilai-Borwein (BB) technique and a specific linear combination of two
previous iterates to accelerate the convergence of modified FPC algorithms. We
demonstrate the effectiveness of our algorithms for computing approximate and
exact rational sum of squares (SOS) decompositions of polynomials with rational
coefficients.

17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg