Polynomial sequences generated by infinite Hessenberg matrices

• Autorzy: Luis Verde-Star
• Języki publikacji: EN

Abstrakty

EN

We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz the polynomial sequences turn out to be of interpolatory type and we obtain additional results. For example, we show that every nonderogative finite square matrix is similar to a unique Toeplitz-Hessenberg matrix.

Słowa kluczowe

EN

Polynomial sequences of interpolatory type; infinite Toeplitz matrices; infinite Hessenberg matrices; Toeplitz companion matrices

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 64-72

Daty

wydano

2017-01-01

otrzymano

2016-08-29

zaakceptowano

2016-09-26

online

2017-01-20

Twórcy

autor

Luis Verde-Star

• Department of Mathematics, Universidad Autónoma Metropolitana, Iztapalapa, Apartado 55-534, México D. F. 09340,,

Identyfikatory

DOI

10.1515/spma-2017-0002