Error analysis of symplectic Lanczos method for Hamiltonian eigenvalue problem

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  • 1.School of Business Administration, North China Electric Power University, Beijing 102206, China; 2.Center of Advanced Design Technology, Dalian University, Dalian 116622, China;

Published date: 05 Sep 2006

Abstract

A rounding error analysis for the symplectic Lanczos method is given to solve the large-scale sparse Hamiltonian eigenvalue problem. If no breakdown occurs in the method, then it can be shown that the Hamiltonian structure preserving requirement does not destroy the essential feature of the nonsymmetric Lanczos algorithm. The relationship between the loss of J-orthogonality among the symplectic Lanczos vectors and the convergence of the Ritz values in the symmetric Lanczos algorithm is discussed. It is demonstrated that under certain assumptions the computed J-orthogonal Lanczos vectors lose the J-orthogonality when some Ritz values begin to converge. Our analysis closely follows the recent works of Bai and Fabbender.

Cite this article

YAN Qingyou, WEI Xiaopeng . Error analysis of symplectic Lanczos method for Hamiltonian eigenvalue problem[J]. Frontiers of Mathematics in China, 2006 , 1(3) : 430 -451 . DOI: 10.1007/s11464-006-0017-7

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