scholarly journals Iterations of linear bounded operators in non self-adjoint eigenvalue problems and Kellogg's iteration process

1962 ◽  
Vol 12 (4) ◽  
pp. 536-554
Author(s):  
Ivo Marek
Keyword(s):  
Eigenvalue Problems ◽  
Iteration Process ◽  
Bounded Operators

On the eigenvalue problem Tu -λ Su =0 with unbounded and nonsymetric operators T and S

1968 ◽  
Vol 262 (1130) ◽  
pp. 413-458 ◽  
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Eigenvalue Problems ◽  
Generalized Method Of Moments ◽  
Elastic Stability ◽  
Theoretical Problem ◽  
Bounded Operators ◽  
Eigenvalues And Eigenvectors ◽  
Complete Section ◽  
Symmetric Operators

In this paper we study both the theoretical problem of the existence and the practical problem of the approximate calculation of eigenvalues and eigenvectors of (i) = 0, where T and S are some linear (in general unbounded and nonhermitian) operators in a Hilbert space. After a short discussion of a class of K -symmetric operators, in section 2 the author proves the existence of eigenvalues and eigenvectors of (i) under various conditions on T and S and investigates conditions under which the set of eigenvectors of (i) is complete. Section 3 indicates briefly the applicability and the unifying property of the generalized method of moments to the approximate solution of (i). Section 4 presents and thoroughly studies a very general new iterative method for the approximate solution of (i). The advantage of this method is that it does not require the practically inconvenient preliminary reduction of (i) to an equivalent problem with bounded operators and that under certain rather general conditions the convergence is mono tonic. Furthermore, by specializing operators and parameters, our iterative method contains as a special case, almost every known iterative method for the calculation of eigenvalues (mostly proved previously only for symmetric matrices and bounded operators). Finally the applicability and the numerical effectiveness of the iterative method is illustrated by calculating the smallest eigenvalue for a selfadjoint and nonselfadjoint eigenvalue problems arising in the problems of elastic stability.

scholarly journals Robust Principal Component Analysis-Based Infrared Small Target Detection

2019 ◽  
Vol 33 ◽  
pp. 9925-9926
Author(s):  
Qiwei Chen ◽  
Cheng Wu ◽  
Yiming Wang
Keyword(s):  
Iteration Process ◽  
Principal Component ◽  
Component Analysis ◽  
Low Rank ◽  
Small Target ◽  
Frame Sequence ◽  
Augmented Lagrange Multiplier ◽  
Small Targets ◽  
Infrared Small Target ◽  
Augmented Lagrange Multiplier Method

A method based on Robust Principle Component Analysis (RPCA) technique is proposed to detect small targets in infrared images. Using the low rank characteristic of background and the sparse characteristic of target, the observed image is regarded as the sum of a low-rank background matrix and a sparse outlier matrix, and then the decomposition is solved by the RPCA. The infrared small target is extracted from the single-frame image or multi-frame sequence. In order to get more efficient algorithm, the iteration process in the augmented Lagrange multiplier method is improved. The simulation results show that the method can detect out the small target precisely and efficiently.

scholarly journals A Revisit to CMFD Schemes: Fourier Analysis and Enhancement

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 424
Author(s):  
Dean Wang ◽  
Zuolong Zhu
Keyword(s):  
Fourier Analysis ◽  
Eigenvalue Problems ◽  
Neutron Transport ◽  
Coarse Mesh ◽  
Successive Overrelaxation ◽  
Computational Cell ◽  
Artificial Diffusion ◽  
Acceleration Method ◽  
The Stability ◽  
Partial Current

The coarse-mesh finite difference (CMFD) scheme is a very effective nonlinear diffusion acceleration method for neutron transport calculations. CMFD can become unstable and fail to converge when the computational cell optical thickness is relatively large in k-eigenvalue problems or diffusive fixed-source problems. Some variants and fixups have been developed to enhance the stability of CMFD, including the partial current-based CMFD (pCMFD), optimally diffusive CMFD (odCMFD), and linear prolongation-based CMFD (lpCMFD). Linearized Fourier analysis has proven to be a very reliable and accurate tool to investigate the convergence rate and stability of such coupled high-order transport/low-order diffusion iterative schemes. It is shown in this paper that the use of different transport solvers in Fourier analysis may have some potential implications on the development of stabilizing techniques, which is exemplified by the odCMFD scheme. A modification to the artificial diffusion coefficients of odCMFD is proposed to improve its stability. In addition, two explicit expressions are presented to calculate local optimal successive overrelaxation (SOR) factors for lpCMFD to further enhance its acceleration performance for fixed-source problems and k-eigenvalue problems, respectively.

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