• Corpus ID: 238583631

Black Box Absolute Reconstruction for Sums of Powers of Linear Forms

@article{Koiran2021BlackBA,
  title={Black Box Absolute Reconstruction for Sums of Powers of Linear Forms},
  author={Pascal Koiran and Subhayan Saha},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.05305}
}
  • P. Koiran, Subhayan Saha
  • Published 11 October 2021
  • Computer Science
  • ArXiv
We study the decomposition of multivariate polynomials as sums of powers of linear forms. We give a randomized algorithm for the following problem: If a homogeneous polynomial f ∈ K[x1, ..., xn] (where K ⊆ C) of degree d is given as a blackbox, decide whether it can be written as a linear combination of d-th powers of linearly independent complex linear forms. The main novel features of the algorithm are: • For d = 3, we improve by a factor of n on the running time from the algorithm in [KS20… 
Derandomization and absolute reconstruction for sums of powers of linear forms
TLDR
An algorithm for the following problem: given a homogeneous polynomial of degree 3, decide whether it can be written as a sum of cubes of linearly independent linear forms with complex coefficients to solve the decomposition of multivariate polynomials as sums of powers of linear forms.

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