Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient evaluation of noncommutative polynomials using tensor and
  noncommutative Waring decompositions   This paper analyses a Waring type decomposition of a noncommuting (NC)
polynomial $p$ with respect to the goal of evaluating $p$ efficiently on tuples
of matrices. Such a decomposition can reduce the number of matrix
multiplications needed to evaluate a noncommutative polynomial and is valuable
when a single polynomial must be evaluated on many matrix tuples.
  In pursuit of this goal we examine a noncommutative analog of the classical
Waring problem and various related decompositions. For example, we consider a
"Waring decomposition" in which each product of linear terms is actually a
power of a single linear NC polynomial or more generally a power of a
homogeneous NC polynomial. We describe how NC polynomials compare to
commutative ones with regard to these decompositions, describe a method for
computing the NC decompositions and compare the effect of various
decompositions on the speed of evaluation of generic NC polynomials.

21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph