The eigenproblem of a tridiagonal 2-Toeplitz matrix
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TLDR
The characteristic polynomial of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the three point Chebyshev recurrence relationship.About:
This article is published in Linear Algebra and its Applications.The article was published on 1994-01-01 and is currently open access. It has received 62 citations till now. The article focuses on the topics: Tridiagonal matrix & Toeplitz matrix.read more
Citations
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Journal ArticleDOI
Matrices: Methods and Applications
TL;DR: The Matrices: Methods and Applications as mentioned in this paper is a collection of matrix-based methods and applications for the analysis of operational R-matrices and its application in the field of network engineering.
Journal ArticleDOI
Explicit inverses of some tridiagonal matrices
C.M. da Fonseca,J. Petronilho +1 more
TL;DR: In this paper, explicit inverses of tridiagonal 2-Toeplitz and 3-Toplitz matrices were given, which generalize some well-known results concerning the inverse of a 2-to-toplitz matrix.
Journal ArticleDOI
Explicit inverse of a tridiagonal k −Toeplitz matrix
C.M. da Fonseca,J. Petronilho +1 more
TL;DR: The proof is based on results from the theory of orthogonal polynomials and it is shown that the entries of the inverse of a nonsingular and irreducible tridiagonal k−Toeplitz matrix A are given in terms of Chebyshev polynmials of the second kind.
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Eigenproblems for tridiagonal 2-Toeplitz matrices and quadratic polynomial mappings
TL;DR: In this article, the eigenvectors of a tridiagonal 2-Toeplitz matrix were shown to be a monic orthogonal polynomial sequence.
Eigenproblems for Tridiagonal2-loeplitz Matrices and Quadratic Polynomial Mappings
F. Marcellin,J. Petronilho +1 more
TL;DR: In this paper, the eigenvectors of a tridiagonal 2-Toeplitz matrix were solved for the case of monastic orthogonal polynomials.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Book
Matrices ' Methods and Applications'
TL;DR: In this article, a basic algebra of matrices is defined, including unique solution of linear equations, determinant and inverse rank, non-unique solution of equations, and applications.
Journal ArticleDOI
Matrices: Methods and Applications
TL;DR: The Matrices: Methods and Applications as mentioned in this paper is a collection of matrix-based methods and applications for the analysis of operational R-matrices and its application in the field of network engineering.
Journal ArticleDOI
Inversion of Toeplitz Matrices which are not Strongly Non-singular
M. J. C. Gover,S. Barnett +1 more
TL;DR: In this paper, the authors introduce a type of matrices appelees r-Tœplitz, and present an algorithm d'inversion with O(rn 2 ) operations.