Computing the Maximal Eigenpairs of Large Size Tridiagonal Matrices with $\mathcal{O}(1)$ Number of Iterations
Year: 2018
Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 4 : pp. 877–894
Abstract
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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2018.s11
Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 4 : pp. 877–894
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
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