The problem of finding the smallest eigenvalue of a real symmetric, positive definite Toeplitz matrix (RSPDTM) is of considerable interest in signal processing. Given the covariance sequence of the observed data, Pisarenko suggested a method which determines the sinusoidal frequencies from the eigenvector of the covariance matrix associated with its minimum eigenvalue. For this reason there are more methods for determination of smallest eigenvalue. These methods can be divided in three large groups: methods based on characteristic polynomial, methods based on secular equation and hybrid methods. It can happen that the smallest eigenvalue of matrix and the smallest eigenvalue of matrix are very close to each other, which can result in very large speed reduction of the second group of methods and in the extreme cases it can result in interruption of algorithm which is based on second group of methods. In this note we bring new strategies for overcoming this problem and we compare algorithms based on these strategies with already existing algorithms. These new strategies are based on mathematical modelling.
Thematic field:
Mehatronika
Opening paper:
Yes
Date:
28.12.2010.
Number of visits:
840
11th International Conference on Accomplishments in Mechanical and Industrial Engineering
Paper file
(8.84 MB)
