@Article{NMTMA-11-877,
author = {Tao Tang and Jiang Yang},
title = {Computing the Maximal Eigenpairs of Large Size Tridiagonal Matrices with $\mathcal{O}(1)$ Number of Iterations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2018},
volume = {11},
number = {4},
pages = {877--894},
abstract = {<p style="text-align: justify;">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&#39;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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2018.s11},
url = {http://global-sci.org/intro/article_detail/nmtma/12477.html}
}