Vol. 28 No. 106 (2004), Mathematics
Vol. 28 No. 106 (2004)

LEVERRIER-FADEEV ALGORITHM AND CLASSICAL ORTHOGONAL POLYNOMIALS

Mathematics
Published 2023-10-11
J. Hernández
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Leganés, Spain.
F. Marcellán
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Leganés, Spain.
C. Rodríguez
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Leganés, Spain.
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Keywords

Characteristic Polynomial
Transfer Functions
Orthogonal Polynomials
Classical Linear Functionals

How to Cite

LEVERRIER-FADEEV ALGORITHM AND CLASSICAL ORTHOGONAL POLYNOMIALS. (2023). Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 28(106), 39-47. https://doi.org/10.18257/raccefyn.28(106).2004.2013
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Abstract

Utilizing structural properties of classical orthogonal polynomials (Hermite, Laguerre, Jacobi, and Bessel), this work presents an implementation of the Leverrier-Fadeev algorithm to derive the characteristic polynomial of a square matrix with complex entries.

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References

S. Barnett, Leverrier’s algorithm for orthogonal polynomials bases, Linear Alg. and Appl. 236 (1996), 245–263.

T. S. Chihara, An introduction to orthogonal polynomials, Gordon and Breach, New York, 1978.

J. S. Frame, Matrix functions and applications IV: Matrix functions and constituent matrices, IEEE Spectrum 1 (1964), 123–131.

F. Marcell ́an, A. Branquinho, & J. C. Petronilho, Classical orthogonal polynomials: A functional approach, Acta Appl. Math. 34 (1994), 283–303.

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