(k, k + 1)-三对角矩阵的双对角化

IF 1 Q2 MATHEMATICS

Special Matrices Pub Date : 2019-01-01 DOI:10.1515/SPMA-2019-0002

S. Takahira, T. Sogabe, T. Usuda

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引用次数: 14

摘要

摘要本文给出了当n < 2k时n × n (k, k+1)-三对角矩阵的双对角化。此外，我们证明了n × n (k, k+1)-三对角矩阵的行列式是对角元素的乘积，并且该矩阵的特征值是对角元素。本文研究了基于[T]中的置换矩阵的快速块对角化算法。Sogabe和M. El-Mikkawy，苹果公司。数学。第一版。[j] .农业工程学报，2011,27(2):444 - 444。Ohashi, T. Sogabe和T. S. Usuda, Int。纯粹与应用。数学。[j].农业工程学报，2016,513-523。

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

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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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.