A TOEPLITZ MATRIX APPROACH TO ANALYZING ZEROS OF REAL POLYNOMIALS IN THE OPEN UNIT DISK

Authors

  • Naima Benmokhtar Djillali Liabes University Author
  • Abderrahmane Larabi Ibn Khaldoun University Author
  • Mohammed said Souid SIMATS; University of Tiaret Author

Keywords:

Sturm sequence, roots of a real polynomial, open unit disk, chebyshev polynomials, a Toeplitz Matrix, cauchy index, sign change, algorithms, linear system

Abstract

In this paper, we propose to improve a numerical method for computing the number of zeros of a real polynomial in the open unit disk, this method is based on the calculation of the generalized Sturm sequence in Chebyshev form. [2] [1]

 For that, we prove that the matrix involved in the calculation of chebychev polynomials is a Toeplitz matrix, furthere we calculate its last line which will be used in this numerical algorithm to make it more efficient.

This numerical method is very important to study the stability of dynamical systems.

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Published

2025-05-07

Issue

Vol. 43 No. 5 (2025)

Section

Articles