Some cases on Strassen additive conjecture
Youngho Woo
TL;DR
This paper investigates the additivity of tensor rank and cactus rank for sums of coprime monomials and bivariate polynomials, extending previous results in the field.
Contribution
It generalizes the additivity results for rank and cactus rank to broader classes of polynomials, including coprime monomials and bivariate cases.
Findings
Additivity of rank verified for coprime monomials and bivariate polynomials.
Similar additivity results established for cactus rank.
Extends previous work on Strassen's additive conjecture.
Abstract
In this article, we verify the additivity for rank of a sum of coprime monomials and bivariate polynomials generalizing the result in (\cite{CCG}). We also show similar results hold for cactus rank.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Tensor decomposition and applications · Polynomial and algebraic computation