Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 877-894.
Published online: 2018-06
[An open-access article; the PDF is free to any online user.]
Cited by
- BibTex
- RIS
- TXT
In a series of papers, Chen [4–6] developed some efficient algorithms for computing the maximal eigenpairs for tridiagonal matrices. The key idea is to explicitly construct effective initials for the maximal eigenpairs and also to employ a self-closed iterative algorithm. In this paper, we extend Chen's algorithm to deal with large scale tridiagonal matrices with super-/sub-diagonal elements. By using appropriate scalings and by optimizing numerical complexity, we make the computational cost for each iteration to be $\mathcal{O}$($N$). Moreover, to obtain accurate approximations for the maximal eigenpairs, the total number of iterations is found to be independent of the matrix size, i.e., $\mathcal{O}$($1$) number of iterations. Consequently, the total cost for computing the maximal eigenpairs is $\mathcal{O}$($N$). The effectiveness of the proposed algorithm is demonstrated by numerical experiments.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2018.s11}, url = {http://global-sci.org/intro/article_detail/nmtma/12477.html} }In a series of papers, Chen [4–6] developed some efficient algorithms for computing the maximal eigenpairs for tridiagonal matrices. The key idea is to explicitly construct effective initials for the maximal eigenpairs and also to employ a self-closed iterative algorithm. In this paper, we extend Chen's algorithm to deal with large scale tridiagonal matrices with super-/sub-diagonal elements. By using appropriate scalings and by optimizing numerical complexity, we make the computational cost for each iteration to be $\mathcal{O}$($N$). Moreover, to obtain accurate approximations for the maximal eigenpairs, the total number of iterations is found to be independent of the matrix size, i.e., $\mathcal{O}$($1$) number of iterations. Consequently, the total cost for computing the maximal eigenpairs is $\mathcal{O}$($N$). The effectiveness of the proposed algorithm is demonstrated by numerical experiments.