Semi-algebraic canonical decomposition of multi-way arrays and Joint Eigenvalue Decomposition

A semi-algebraic algorithm based on Joint Eigenvalue De composition (JEVD) is proposed to compute the CP de composition of multi-way arrays. The iterative part of the method is thus limited to the JEVD computation. In addition it involves less restrictive hypothesis than other recent semi algebraic approaches. We also propose an original JEVD technique based on the LU factorization. Numerical examples highlight the main advantages of the proposed methods to solve both the JEVD and CP problems.