Eigenvalue problem of a large scale indefinite gyroscopic dynamic system

2006 ◽  
Vol 27 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Yong-feng Sui ◽  
Wan-xie Zhong
Keyword(s):  
Eigenvalue Problem ◽  
Dynamic System ◽  
Large Scale

scholarly journals A spectroscopic census of the Fornax cluster and beyond: preparing for next generation surveys

2019 ◽  
Vol 490 (2) ◽  
pp. 1666-1677 ◽  
Author(s):  
Natasha Maddox ◽  
Paolo Serra ◽  
Aku Venhola ◽  
Reynier Peletier ◽  
Ilani Loubser ◽  
...  
Keyword(s):  
Dynamic System ◽  
Southern Hemisphere ◽  
Large Scale ◽  
Near Infrared ◽  
State Of The Art ◽  
Large Scale Structure ◽  
Large Cluster ◽  
Cluster Membership ◽  
The Many ◽  
Fornax Cluster

ABSTRACT The Fornax cluster is the nearest large cluster in the southern sky, and is currently experiencing active assembly of mass. It is thus the target of a number of ongoing observing campaigns at optical, near-infrared, and radio wavelengths, using state-of-the-art facilities in the Southern hemisphere. Spectroscopic redshifts are essential not only for determining cluster membership, but also kinematics within the cluster and identifying substructures. We present a compilation of all available major spectroscopic campaigns undertaken within the Fornax region, including new and previously unpublished spectroscopy. This provides not only a comprehensive census of Fornax cluster membership as a resource for the many ongoing studies of this dynamic system, but also probes the large-scale structure in the background volume.

Analysis of vibration levels of large structural system with recursive component mode synthesis method: Theory and convergence

2006 ◽  
Vol 220 (9) ◽  
pp. 1339-1345 ◽  
Author(s):  
C W Kim
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Large Scale ◽  
Synthesis Method ◽  
Lanczos Method ◽  
Component Mode Synthesis ◽  
Structural System ◽  
Accurate Analysis ◽  
Satisfactory Performance ◽  
And Performance

The component mode synthesis (CMS) method has been extensively used in industries. However, industry finite-element (FE) models need a more efficient CMS method for satisfactory performance since the size of FE models needs to be increased for a more accurate analysis. Recently, the recursive component mode synthesis (RCMS) method was introduced to solve large-scale eigenvalue problem efficiently. This article focuses on the convergence of the RCMS method with respect to different parameters, and evaluates the accuracy and performance compared with the Lanczos method.

Dynamic Synthesis/Design and Operation/Control Optimization Under Uncertainty of a PEMFC System

2008 ◽  
Author(s):  
Kihyung Kim ◽  
Meng Wang ◽  
Michael R. von Spakovsky ◽  
Douglas J. Nelson
Keyword(s):  
Dynamic System ◽  
Alternative Energy ◽  
Large Scale ◽  
Proton Exchange ◽  
Optimization Under Uncertainty ◽  
Cost Models ◽  
System Synthesis ◽  
Control Optimization ◽  
Synthesis Design ◽  
Operation Control

Proton exchange membrane fuel cells (PEMFCs) are one of the leading candidates in alternative energy conversion devices for transportation, stationary, and portable power generation applications. Such systems with their own fuel conversion unit typically consist of several subsystems: a fuel processing subsystem, a fuel cell stack subsystem, a work recovery-air supply subsystem, and a power electronics subsystem. Since these subsystems have different physical characteristics, their integration into a single system/subsystem level unit make the problems of optimal dynamic system synthesis/design and operation/control highly complex. Thus, dynamic system/subsystem/component modeling and highly effective optimization strategies are required. Furthermore, uncertainties in the results of system synthesis/design and operation/control optimization can be affected by any number of sources of uncertainty such as the load profiles and cost models. These uncertainties can be taken into account by treating the problem probabilistically. The difficulty with doing this, particularly when large-scale dynamic optimization with a large number of degrees of freedom is being used to determine the optimal synthesis/design and operation/control of the system, is that the traditional probabilistic approaches (e.g., Monte Carlo Method) are so computationally intensive that combined with large-scale optimization it renders the problem computationally intractable. This difficulty can be overcome by the use of approximate approaches such as the response sensitivity analysis (RSA) method based on Taylor series expansion. Thus, in this paper, a stochastic modeling and uncertainty analysis methodology for energy system synthesis/design and operation/control which uses the RSA method is proposed and employed for calculating the uncertainties on the system outputs. Their effects on the synthesis/design and operation/control optimization of a 5kWe PEMFC system are assessed by taking the uncertainties into account in the objectives and constraints. It is shown that these uncertainties significantly affect the reliability of being able to meet certain constraints (e.g., that on the CO concentration) during the synthesis/design and operation/control optimization process. These and other results are presented.

New scheme for large-scale eigenvalue problems of the RPA-type matrix equation

1992 ◽  
Vol 70 (2) ◽  
pp. 296-300 ◽  
Author(s):  
Susumu Narita ◽  
Tai-ichi Shibuya
Keyword(s):  
Eigenvalue Problem ◽  
Convergence Rate ◽  
Matrix Equation ◽  
Large Scale ◽  
Eigenvalue Problems ◽  
Type Equation ◽  
Fast Convergence ◽  
New Method ◽  
Eigenvalues And Eigenvectors ◽  
Numerical Tests

A new method is proposed for obtaining a few eigenvalues and eigenvectors of a large-scale RPA-type equation. Some numerical tests are carried out to study the convergence behaviors of this method. It is found that the convergence rate is very fast and quite satisfactory. It depends strongly on the way of estimating the deviation vectors. Our proposed scheme gives a better estimation for the deviation vectors than Davidson's scheme. This scheme is applicable to the eigenvalue problems of nondiagonally dominant matrices as well. Keywords: large-scale eigenvalue problem, RPA-type equation, fast convergence.

scholarly journals Numerical Algorithms for Computing an Arbitrary Singular Value of a Tensor Sum

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 211
Author(s):  
Asuka Ohashi ◽  
Tomohiro Sogabe
Keyword(s):  
Eigenvalue Problem ◽  
Large Scale ◽  
Numerical Algorithms ◽  
Direct Methods ◽  
Coefficient Matrix ◽  
Lanczos Method ◽  
Singular Value ◽  
Preconditioned Conjugate Gradient ◽  
Schur Decomposition ◽  
Pcg Method

We consider computing an arbitrary singular value of a tensor sum: T:=In⊗Im⊗A+In⊗B⊗Iℓ+C⊗Im⊗Iℓ∈Rℓmn×ℓmn, where A∈Rℓ×ℓ, B∈Rm×m, C∈Rn×n. We focus on the shift-and-invert Lanczos method, which solves a shift-and-invert eigenvalue problem of (TTT−σ˜2Iℓmn)−1, where σ˜ is set to a scalar value close to the desired singular value. The desired singular value is computed by the maximum eigenvalue of the eigenvalue problem. This shift-and-invert Lanczos method needs to solve large-scale linear systems with the coefficient matrix TTT−σ˜2Iℓmn. The preconditioned conjugate gradient (PCG) method is applied since the direct methods cannot be applied due to the nonzero structure of the coefficient matrix. However, it is difficult in terms of memory requirements to simply implement the shift-and-invert Lanczos and the PCG methods since the size of T grows rapidly by the sizes of A, B, and C. In this paper, we present the following two techniques: (1) efficient implementations of the shift-and-invert Lanczos method for the eigenvalue problem of TTT and the PCG method for TTT−σ˜2Iℓmn using three-dimensional arrays (third-order tensors) and the n-mode products, and (2) preconditioning matrices of the PCG method based on the eigenvalue and the Schur decomposition of T. Finally, we show the effectiveness of the proposed methods through numerical experiments.

scholarly journals Trace minimization method via penalty for linear response eigenvalue problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yadan Chen ◽  
Yuan Shen ◽  
Shanshan Liu
Keyword(s):  
Eigenvalue Problem ◽  
Linear Response ◽  
Large Scale ◽  
Eigenvalue Problems ◽  
Minimum Principle ◽  
Gradient Descent Method ◽  
Step Size ◽  
Minimization Method ◽  
Energy Excitation ◽  
Orthogonality Constraint

<p style='text-indent:20px;'>In various applications, such as the computation of energy excitation states of electrons and molecules, and the analysis of interstellar clouds, the linear response eigenvalue problem, which is a special type of the Hamiltonian eigenvalue problem, is frequently encountered. However, traditional eigensolvers may not be applicable to this problem owing to its inherently large scale. In fact, we are usually more interested in computing some of the smallest positive eigenvalues. To this end, a trace minimum principle optimization model with orthogonality constraint has been proposed. On this basis, we propose an unconstrained surrogate model called trace minimization via penalty, and we establish its equivalence with the original constrained model, provided that the penalty parameter is larger than a certain threshold. By avoiding the orthogonality constraint, we can use a gradient-type method to solve this model. Specifically, we use the gradient descent method with Barzilai–Borwein step size. Moreover, we develop a restarting strategy for the proposed algorithm whereby higher accuracy and faster convergence can be achieved. This is verified by preliminary experimental results.</p>

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