TY - JOUR
T1 - Computing the Maximal Eigenpairs of Large Size Tridiagonal Matrices with $\mathcal{O}(1)$ Number of Iterations
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 877
EP - 894
PY - 2018
DA - 2018/06
SN - 11
DO - http://doi.org/10.4208/nmtma.2018.s11
UR - https://global-sci.org/intro/article_detail/nmtma/12477.html
KW - 
AB - <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>