scholarly journals A Subspace Method for Large-Scale Eigenvalue Optimization

2018 ◽  
Vol 39 (1) ◽  
pp. 48-82 ◽  
Author(s):  
Fatih Kangal ◽  
Karl Meerbergen ◽  
Emre Mengi ◽  
Wim Michiels
Keyword(s):  
Large Scale ◽  
Eigenvalue Optimization ◽  
Subspace Method

scholarly journals Large-Scale Computation of $\mathcal{L}_\infty$-Norms by a Greedy Subspace Method

2017 ◽  
Vol 38 (4) ◽  
pp. 1496-1516 ◽  
Author(s):  
Nicat Aliyev ◽  
Peter Benner ◽  
Emre Mengi ◽  
Paul Schwerdtner ◽  
Matthias Voigt
Keyword(s):  
Large Scale ◽  
Subspace Method

SUBSPACE METHOD FOR ANALYZING LARGE-SCALE NONLINEAR STOCHASTIC DYNAMIC SYSTEMS WITH POLYNOMIAL TYPE OF NONLINEARITES

2012 ◽  
Vol 09 (01) ◽  
pp. 1240017 ◽  
Author(s):  
G. K. ER ◽  
V. P. IU
Keyword(s):  
Dynamic Systems ◽  
Large Scale ◽  
Gaussian White Noise ◽  
The State ◽  
Stochastic Dynamic ◽  
Subspace Method ◽  
State Variables ◽  
Polynomial Type ◽  
Fpk Equation ◽  
Stochastic Dynamic Systems

In this paper, the probabilistic solutions of the multi-degree-of-freedom (MDOF) or large-scale stochastic dynamic systems with polynomial type of nonlinearity and excited by Gaussian white noise excitations are obtained and investigated with the subspace method proposed recently by the authors. The space of the state variables of large-scale nonlinear stochastic dynamic (NSD) system excited by white noises is separated into two subspaces. Both sides of the Fokker–Planck–Kolmogorov (FPK) equation corresponding to the NSD system is then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in another subspace is formulated. Therefore, the FPK equation in low dimensions is obtained from the original FPK equation in high dimensions and it makes the problem of obtaining the probabilistic solutions of large-scale NSD systems solvable with the exponential polynomial closure (EPC) method. A simple flexural beam on nonlinear elastic springs is analyzed with the subspace method to show the effectiveness of the subspace-EPC method in this case.

A TRUST REGION SUBSPACE METHOD FOR LARGE-SCALE UNCONSTRAINED OPTIMIZATION

2012 ◽  
Vol 29 (04) ◽  
pp. 1250021 ◽  
Author(s):  
LUJIN GONG
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Trust Region ◽  
Numerical Results ◽  
Subspace Method ◽  
Large Scale Unconstrained Optimization ◽  
Unconstrained Problems

This paper presents a trust region subspace method for minimizing large-scale unconstrained problems. We choose a subspace that consists of some old directions which are invariable and some newest directions which are changed at each iteration. A restart technique is used when the old directions have little contribution. Numerical results are reported which indicate that the method is promising.

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