# 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} }

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…

## One Citation

Derandomization and absolute reconstruction for sums of powers of linear forms

- Computer Science, MathematicsTheor. Comput. Sci.
- 2021

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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