The Tridiagonal Approach to Szegö’s Orthogonal Polynomials, Toeplitz Linear Systems, and Related Interpolation Problems

1988 ◽  
Vol 19 (3) ◽  
pp. 718-735 ◽  
Author(s):  
P. Delsarte ◽  
Y. Genin
Keyword(s):  
Orthogonal Polynomials ◽  
Linear Systems ◽  
Interpolation Problems

scholarly journals New Stability Criteria for Discrete Linear Systems Based on Orthogonal Polynomials

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1322
Author(s):  
Luis E. Garza ◽  
Noé Martínez ◽  
Gerardo Romero
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Linear Systems ◽  
Real Line ◽  
Stability Criteria ◽  
The Real ◽  
Discrete Linear Systems ◽  
New Criterion ◽  
Schur Stability

A new criterion for Schur stability is derived by using basic results of the theory of orthogonal polynomials. In particular, we use the relation between orthogonal polynomials on the real line and on the unit circle known as the Szegő transformation. Some examples are presented.

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