A SEQUENTIAL SUBSPACE PROJECTION METHOD FOR LINEAR SYMMETRIC EIGENVALUE PROBLEM

Xin Liu (), Chunlin Hao () and Minghou Cheng ()
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Xin Liu: State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China
Chunlin Hao: Beijing University of Technology, Beijing 100124, P. R. China
Minghou Cheng: Huada Empyrean Software Co., Ltd., Beijing 100102, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2013, vol. 30, issue 03, 1-17

Abstract: In this paper, we introduce a geometric model for linear symmetric eigenvalue problem, which is motivated by the fact that any eigenvalue of a symmetric positive definite matrix A is the reciprocal of the square length of an axis of the ellipsoid xTAx = 1. Hence, to find the largest eigenvalue is equivalent to calculate the shortest axis of the corresponding ellipsoid. Two sequential subspace projection algorithms based on this idea are proposed, and we establish the global convergence and local linear convergence rate of our proposed algorithms. Numerical experiments demonstrate that our algorithm outperforms the MATLAB built-in solver "EIGS" which calls the famous package "ARPACK".

Keywords: Sequential subspace projection method; linear eigenvalue problem; Rayleigh–Ritz quotient; global convergence; linear convergence rate; 65K05; 90C26; 65F15 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1142/S0217595913400034

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