EIGENVECTOR

作品数：79被引量：90H指数：4
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ACCELERATED OPTIMIZATION WITH ORTHOGONALITY CONSTRAINTS被引量：1
《Journal of Computational Mathematics》2021年第2期207-226,共20页Jonathan W.Siegel 
We develop a generalization of Nesterov’s accelerated gradient descent method which is designed to deal with orthogonality constraints.To demonstrate the effectiveness of our method,we perform numerical experiments w...
关键词：Riemannian optimization Stiefel manifold Accelerated gradient descent Eigenvector problems Electronic structure calculations 
INEXACT TWO-GRID METHODS FOR EIGENVALUE PROBLEMS
《Journal of Computational Mathematics》2015年第6期557-575,共19页Qun Gu Weiguo Gao 
The authors are grateful to Prof. Zhaojun Bai in University of Cali- fornia, Davis, and Prof. Carlos J. Garcia-Cervera in University of California, Santa Barbara for their helpful discussions. The authors are grateful to the editor and the referees for their valuable comments, which improves the quality of the paper greatly. Weiguo Gao is supported by the National Natural Science Foundation of China under grants 91330202, Special Funds for Major State Basic Research Projects of China （2015CB858560003）, and Shanghai Science and Technology Development Funds 13dz2260200 and 13511504300. Qun Gu acknowledges the financial support from China Scholarship Council （No. 2011610055）.
We discuss the inexact two-grid methods for solving eigenvalue problems, including both partial differential and integral equations. Instead of solving the linear system exactly in both traditional two-grid and accele...
关键词：INEXACT Two-grid EIGENVALUE EIGENVECTOR Finite element method Conver-gence rate. 
BLOCK-SYMMETRIC AND BLOCK-LOWER-TRIANGULAR PRECONDITIONERS FOR PDE-CONSTRAINED OPTIMIZATION PROBLEMS＊被引量：3
《Journal of Computational Mathematics》2013年第4期370-381,共12页Guofeng Zhang Zhong Zheng 
Acknowledgments. This work was supported by the National Natural Science Foundation of China（l1271174）. The authors are very much indebted to the referees for providing very valuable suggestions and comments, which greatly improved the original manuscript of this paper. The authors would also like to thank Dr. Zeng-Qi Wang for helping on forming the MATLAB data of the matrices.
Optimization problems with partial differential equations as constraints arise widely in many areas of science and engineering, in particular in problems of the design. The solution of such class of PDE-constrained op...
关键词：Saddle-point matrix PRECONDITIONING PDE-constrained optimization Eigen-value and eigenvector Regularization parameter. 
COMPUTING EIGENVECTORS OF NORMAL MATRICES WITH SIMPLE INVERSE ITERATION被引量：1
《Journal of Computational Mathematics》2003年第5期657-670,共14页Zhen-yue Zhang Tiang-wei Ouyang (Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou 310027, China) 
The work of this author was supported in part by NSFC (project 19771073);Special Funds for Major State Basic Research Projects of China (project G19990328); Zhejiang Provincial Natural Science Foundation of China;Foundation for University Key Te
It is well-known that if we have an approximate eigenvalue A of a normal matrix A of order n, a good approximation to the corresponding eigenvector u can be computed by one inverse iteration provided the position, say...
关键词：EIGENVECTOR Inverse iteration ACCURACY Error estimation. 
PRECONDITIONING BLOCK LANCZOS ALGORITHM FOR SOLVING SYMMETRIC EIGENVALUE PROBLEMS被引量：7
《Journal of Computational Mathematics》2000年第4期365-374,共10页Hua Dai Peter Lancaster 
National Natural Science Foundation of China;Jiangsu Province Natural Science Foundation;Jiangsu Province "333 Engineering
A preconditioned iterative method for computing a few eigenpairs of large sparse symmetric matrices is presented in this paper. The proposed method which combines the preconditioning techniques with the efficiency of ...
关键词：EIGENVALUE EIGENVECTOR sparse matrices Lanczos method PRECONDITIONING 
IMPROVING EIGENVECTORS IN ARNOLDI'S METHOD被引量：4
《Journal of Computational Mathematics》2000年第3期265-276,共12页Zhong-xiao Jia (Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China) Ludwig Elsner (Fakultat fur Mathematik, University Bielefeld, Postfach 100131, 33501 Bielefeld,Germany) 
the China State Key Project for Basic Researches;the National Natural Science Foundation of China;The Research Fund for th
The Ritz vectors obtained by Arnoldi's method may not be good approxima- tions and even may not converge even if the corresponding Ritz values do. In order to improve the quality of Ritz vectors and enhance the effic...
关键词：Large unsymmetric The m-step Arnoldi process The m-step Arnoldi method EIGENVALUE Ritz value EIGENVECTOR Ritz vector Modified 
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