Canonical decomposition of even order hermitian positive semi-definite arrays

Most of the algorithms today available to compute the canonical decomposition of higher order arrays are either computationally very heavy, or are not guaranteed to converge to the global optimum. The solution we propose in order to keep the numerical complexity moderate is i) to stop the latter alg...

Full description

Saved in:
Bibliographic Details
Main Authors: Karfoul, A., Albera, L., Comon, P.
Format: Conference Proceeding
Language:English
Subjects:
Algorithms
Arrays
Computation
Computer simulation
Computers
Cost function
Decomposition
Indium phosphide
Jacobian matrices
Mathematical models
Matlab
Matrix decomposition
Nickel
Optimization
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Most of the algorithms today available to compute the canonical decomposition of higher order arrays are either computationally very heavy, or are not guaranteed to converge to the global optimum. The solution we propose in order to keep the numerical complexity moderate is i) to stop the latter algorithms once the solution belongs to the convergence region of the global optimum, and ii) to refine the solution with a mere gradient descent algorithm. The case of fourth order hermitian positive semi-definite arrays with complex entries is considered. In fact, the hermitian symmetry constraint is taken into account by optimizing a higher order multivariate polynomial criterion. A compact matrix form of the gradient is then computed based on an appropriate framework allowing for derivation in ℂ whereas the cost function is not complex analytic. This compact expression is perfectly suitable for matrix-based programming environments such as MATLAB where loops are to be avoided at all costs. Eventually, computer results show a good performance of the proposed approach.