Queueing models, block hessenberg matrices and the method of neuts

1987 ◽  
Vol 8 (1) ◽  
pp. 265-284
Author(s):  
Wei-Lu Cao ◽  
W. J. Stewart
Keyword(s):  
Queueing Models ◽  
Hessenberg Matrices ◽  
Block Hessenberg Matrices

scholarly journals Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Luis Verde-Star
Keyword(s):  
Triangular Matrix ◽  
Identity Matrix ◽  
Lower Triangular Matrix ◽  
Triangular Matrices ◽  
Hessenberg Matrices ◽  
Banded Matrices ◽  
Lower Triangular ◽  
And Inversion ◽  
Block Hessenberg Matrices ◽  
Explicit Expressions

AbstractWe use elementary triangular matrices to obtain some factorization, multiplication, and inversion properties of triangular matrices. We also obtain explicit expressions for the inverses of strict k-Hessenberg matrices and banded matrices. Our results can be extended to the cases of block triangular and block Hessenberg matrices. An n × n lower triangular matrix is called elementary if it is of the form I + C, where I is the identity matrix and C is lower triangular and has all of its nonzero entries in the k-th column,where 1 ≤ k ≤ n.

Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle

2021 ◽  
Vol 71 (2) ◽  
pp. 341-358
Author(s):  
Edinson Fuentes ◽  
Luis E. Garza
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Matrix Transformations ◽  
Spectral Matrix ◽  
Orthonormal Polynomials ◽  
Matrix Orthogonal Polynomials ◽  
Hessenberg Matrices ◽  
Spectral Transformations ◽  
Block Hessenberg Matrices

Abstract In this contribution, we study properties of block Hessenberg matrices associated with matrix orthonormal polynomials on the unit circle. We also consider the Uvarov and Christoffel spectral matrix transformations of the orthogonality measure, and obtain some relations between the associated Hessenberg matrices.

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