Bidiagonalization of (k, k + 1)-tridiagonal matrices

Bidiagonalization of (k, k + 1)-tridiagonal matrices

In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix are the diagonal elements. This paper is rela...

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Bibliographic Details
Main Authors: Takahira S., Sogabe T., Usuda T.S.
Format: Article
Language:English
Published: De Gruyter 2019-01-01
Series:Special Matrices
Subjects:
(k
k + 1)-tridiagonal matrix
bidiagonalization
eigenvalues
primary 65f15
secondary 65f30
Online Access:https://doi.org/10.1515/spma-2019-0002
Description
Summary:In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix are the diagonal elements. This paper is related to the fast block diagonalization algorithm using the permutation matrix from [T. Sogabe and M. El-Mikkawy, Appl. Math. Comput., 218, (2011), 2740-2743] and [A. Ohashi, T. Sogabe, and T. S. Usuda, Int. J. Pure and App. Math., 106, (2016), 513-523].
ISSN:2300-7451

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