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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (5) : 222-225.

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Abstract

Abstract: In this paper, the Lanczos-QR algorithm was introduced into the computation of the large complex eigenvalue problem. This method, which combines the efficiency of the Lanczos algorithm and the stability of the QR algorithm, firstly reduces the matrix scale with the Lanczos algorithm, and then solves the complex eigenvalues and the complex eigenvectors of the reduced matrix with the QR algorithm. In order to improve the algorithm’s computing stability and precision, the partitioned matrix triangle decomposition was introduced to achieve the standard eigenvalue problem. A step-by step procedure of this method was summarized and programmed in FORTRAN language. Numerical examples show that the improved Lanczos-QR algorithm is precise and stable.