Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Sparse SOS Decomposition Algorithm Based on Term Sparsity   A new sparse SOS decomposition algorithm is proposed based on a new sparsity
pattern, called cross sparsity patterns. The new sparsity pattern focuses on
the sparsity of terms and thus is different from the well-known correlative
sparsity pattern which focuses on the sparsity of variables though the sparse
SOS decomposition algorithms based on these two sparsity patterns both take use
of chordal extensions/chordal decompositions. Moreover, it is proved that the
SOS decomposition obtained by the new sparsity pattern is always a refinement
of the block-diagonalization obtained by the sign-symmetry method. %Because the
new sparsity pattern covers more sparse polynomials than correlative sparsity
pattern, Various experiments show that the new algorithm dramatically saves the
computational cost compared to existing tools and can handle some really huge
polynomials.

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The categories of this paper are: physics
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio