About polynomial matrix-function spectral factorization algorithm

Author: Giorgi Rukhaia
Keywords: Polynomial matrix, spectral factorization, wilson's method, cholesky decomposition for nonnegative matrices
Annotation:

This bachelor thesis describes new algorithm of spectral factorization for polynomial matrix-functions. This algorithm is based on the recently published proof of spectral factorization existence theorem. Software implementation was created. While creating program, thoroughly was studied Wilsons method for scalar factorization and it’s improvement, which plays essential role for fast and effective solution of final problem. Newest methods for complex polynomial root finding were searched and studied together with their implementations. Cholesky factorization for positively defined matrices was studied and improved to work on positive semidefinite matrices.

Lecture files:

პრეზენტაცია [ka]
პოლინომიალური მატრიც-ფუნქციის სპექტრალური ფაქტორიზაციის ალგორითმის შესახებ [ka]