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Bidiagonalization of (k, k + 1)-tridiagonal matrices
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Abstract
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].
Title: Bidiagonalization of (k, k + 1)-tridiagonal matrices
Description:
Abstract
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].
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