Reconstruction of a homogeneous polynomial from its additive decompositions when identifiability fails
Let X⊂ℙr be an integral and non-degenerate complex variety. For any q∈ℙr let rX(q) be its X-rank and S(X,q) the set of all finite subsets of X such that |S|=rX(q) and q ∈ 〈S〉, where 〈〉 denotes the linear span. We consider the case |S(X,q)|>1 (i.e. when q is not X -identifiable) and study the s...
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Format: | Article |
Language: | English |
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Emerald Publishing
2021-04-01
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Series: | Arab Journal of Mathematical Sciences |
Subjects: | |
Online Access: | https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.09.001/full/pdf |
Summary: | Let X⊂ℙr be an integral and non-degenerate complex variety. For any q∈ℙr let rX(q) be its X-rank and S(X,q) the set of all finite subsets of X such that |S|=rX(q) and q ∈ 〈S〉, where 〈〉 denotes the linear span. We consider the case |S(X,q)|>1 (i.e. when q is not X -identifiable) and study the set W(X)q:=∩ S∈S(X,q)〈S〉, which we call the non-uniqueness set of q. We study the case dimX=1 and the case X a Veronese embedding of ℙn. We conclude the paper with a few remarks concerning this problem over the reals. |
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ISSN: | 1319-5166 2588-9214 |