Efficient computation of tridiagonal matrices largest eigenvalue

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:330

Article

Coelho, Diego F. G.¹  Dimitrov, Vassil S.^1,2  Rakai, L.¹ 

[1] Univ Calgary, Elect & Comp Engn Dept, Calgary, AB, Canada

[2] Comp Modelling Grp, Calgary, AB, Canada

关键词: Eigenvalue;    Tridiagonal matrix;    Fast algorithm;    Power method;   

DOI  :  10.1016/j.cam.2017.08.008

来源: Elsevier

【 摘 要 】

This paper proposes a method for a fast estimation of the largest eigenvalue of an asymmetric tridiagonal matrix. The proposed method is based on the Power method and the computation of the square of the original matrix. The matrix square is computed through a proposed fast algorithm designed specifically for tridiagonal matrices. Implementations for compressed column (CCS) and compressed row storage (CRS) formats are provided, discussed and compared to a standard scientific library. We investigate the roundoff numerical errors, showing that the proposed method provides errors no greater than the usual Power method. We provide numerical results with simulations in C/C++ implementation in order to demonstrate the effectiveness of the proposed method. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free