On the Problem of Decoupling Multivariate Polynomials
- 77 Downloads
In this paper we address the application properties of the decoupling multivariate polynomials problem algorithm proposed in . By numerous examples we demonstrate that this algorithm, unfortunately, fails to provide a solution in some cases. Therefore we empirically determine the application scope of this algorithm and show that it is connected with the uniqueness conditions of the CP-decomposition (Canonical Polyadic Decomposition). We also investigate the approximation properties of this algorithm and show that it is capable of construction the best low-rank polynomial approximation provided that the CP-decomposition is unique.
KeywordsLow-parametric representation Polynomial Tensor decomposition
The work was supported by the Russian Science Foundation, grant 19-11-00338.
- 8.Kruskal, J.B.: Rank decomposition, and uniqueness for 3-way and N-way arrays. In: Coppi, R., Bolasco, S. (eds.) Multiway Data Analysis, pp. 8–18. North-Holland, Amsterdam (1988)Google Scholar