Based on damping blocked inverse power method,a type of generalized parallel conjugate gradient method is proposed for large scale eigenvalue problems.Techniques for orthogonalization and computing Rayleigh-Ritz probl...Based on damping blocked inverse power method,a type of generalized parallel conjugate gradient method is proposed for large scale eigenvalue problems.Techniques for orthogonalization and computing Rayleigh-Ritz problems are introduced to improve the stability,efficiency and scalability.Furthermore,a computing package is built based on the proposed method here.Some numerical tests are provided to validate the stability,efficiency and scalability of the method in this paper.The corresponding computing package can be downloaded from the web site:https://githu b.com/pase2017/GCGE-1.0.展开更多
In this paper,we introduce some strategies to improve the efficiency and scalability of the generalized conjugate gradient algorithm and build a package GCGE for solving large scale eigenvalue problems.This method is ...In this paper,we introduce some strategies to improve the efficiency and scalability of the generalized conjugate gradient algorithm and build a package GCGE for solving large scale eigenvalue problems.This method is the combination of damping idea,subspace projection method and inverse power algorithm with dynamic shifts.To reduce the dimensions of projection subspaces,a moving mechanism is developed when the number of desired eigenpairs is large.The numerical methods,implementing techniques and the structure of the package are presented.Plenty of numerical results are provided to demonstrate the efficiency,stability and scalability of the concerned eigensolver and the package GCGE for computing many eigenpairs of large symmetric matrices arising from applications.展开更多
We consider the problem of minimizing the average of a large number of smooth component functions over one smooth inequality constraint.We propose and analyze a stochastic Moving Balls Approximation(SMBA)method.Like s...We consider the problem of minimizing the average of a large number of smooth component functions over one smooth inequality constraint.We propose and analyze a stochastic Moving Balls Approximation(SMBA)method.Like stochastic gradient(SG)met hods,the SMBA method's iteration cost is independent of the number of component functions and by exploiting the smoothness of the constraint function,our method can be easily implemented.Theoretical and computational properties of SMBA are studied,and convergence results are established.Numerical experiments indicate that our algorithm dramatically outperforms the existing Moving Balls Approximation algorithm(MBA)for the structure of our problem.展开更多
基金supported by Science Challenge Project(No.TZ2016002)National Natural Science Foundations of China(NSFC 11771434,91730302)the National Center for Mathematics and Interdisciplinary Science,CAS.
文摘Based on damping blocked inverse power method,a type of generalized parallel conjugate gradient method is proposed for large scale eigenvalue problems.Techniques for orthogonalization and computing Rayleigh-Ritz problems are introduced to improve the stability,efficiency and scalability.Furthermore,a computing package is built based on the proposed method here.Some numerical tests are provided to validate the stability,efficiency and scalability of the method in this paper.The corresponding computing package can be downloaded from the web site:https://githu b.com/pase2017/GCGE-1.0.
基金supported partly by National Key R&D Program of China 2019YFA0709600,2019YFA0709601,Science Challenge Project(No.TZ2016002)the National Center for Mathematics and Interdisciplinary Science,CAS,and Tianjin Education Commission Scientific Research Plan(2017KJ236).
文摘In this paper,we introduce some strategies to improve the efficiency and scalability of the generalized conjugate gradient algorithm and build a package GCGE for solving large scale eigenvalue problems.This method is the combination of damping idea,subspace projection method and inverse power algorithm with dynamic shifts.To reduce the dimensions of projection subspaces,a moving mechanism is developed when the number of desired eigenpairs is large.The numerical methods,implementing techniques and the structure of the package are presented.Plenty of numerical results are provided to demonstrate the efficiency,stability and scalability of the concerned eigensolver and the package GCGE for computing many eigenpairs of large symmetric matrices arising from applications.
文摘We consider the problem of minimizing the average of a large number of smooth component functions over one smooth inequality constraint.We propose and analyze a stochastic Moving Balls Approximation(SMBA)method.Like stochastic gradient(SG)met hods,the SMBA method's iteration cost is independent of the number of component functions and by exploiting the smoothness of the constraint function,our method can be easily implemented.Theoretical and computational properties of SMBA are studied,and convergence results are established.Numerical experiments indicate that our algorithm dramatically outperforms the existing Moving Balls Approximation algorithm(MBA)for the structure of our problem.
