An efficient algorithm for the Schrödinger–Poisson eigenvalue problem

In this paper, we consider the eigenproblems for Latin squares in a bipartite min-max-plus system. The focus is upon developing a new algorithm to compute the eigenvalue and eigenvectors (trivial and non-trivial) for Latin squares in a bipartite min-max-plus system. We illustrate the algorithm using some examples. The proposed algorithm is implemented in MATLAB, using max-plus algebra toolbox. Computationally speaking, our algorithm has a clear advantage over the power algorithm presented by Subiono and van der Woude. Because our algorithm takes 0 . 088783 sec to solve the eigenvalue problem for Latin square presented in Example 2, while the compared one takes 1 . 718662 sec for the same problem. Furthermore, a time complexity comparison is presented, which reveals that the proposed algorithm is less time consuming when compared with some of the existing algorithms.

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A Combination of Modal Synthesis and Subspace Iteration for an Efficient Algorithm for Modal Analysis within a FE-Code

Shock and Vibration ◽

10.1155/2003/147898 ◽

2003 ◽

Vol 10 (1) ◽

pp. 27-35 ◽

Cited By ~ 1

Author(s):

M.W. Zehn

Keyword(s):

Eigenvalue Problem ◽

Modal Analysis ◽

Efficient Algorithm ◽

Degrees Of Freedom ◽

Synthesis Method ◽

Problem Solver ◽

Synthesis Methods ◽

Combined Method ◽

Subspace Iteration ◽

Modal Synthesis

Various well-known modal synthesis methods exist in the literature, which are all based upon certain assumptions for the relation of generalised modal co-ordinates with internal modal co-ordinates. If employed in a dynamical FE substructure/superelement technique the generalised modal co-ordinates are represented by the master degrees of freedom (DOF) of the master nodes of the substructure. To conduct FE modal analysis the modal synthesis method can be integrated to reduce the number of necessary master nodes or to ease the process of defining additional master points within the structure. The paper presents such a combined method, which can be integrated very efficiently and seamless into a special subspace eigenvalue problem solver with no need to alter the FE system matrices within the FE code. Accordingly, the merits of using the new algorithm are the easy implementation into a FE code, the less effort to carry out modal synthesis, and the versatility in dealing with superelements. The paper presents examples to illustrate the proper work of the algorithm proposed.

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Computational Micrograph Registration with Sieve Processes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164660 ◽

1996 ◽

Vol 54 ◽

pp. 440-441

Author(s):

P.J. Phillips ◽

J. Huang ◽

S. M. Dunn

Keyword(s):

Planar Graph ◽

Efficient Algorithm ◽

Spatial Organization ◽

Spatial Arrangement ◽

Stereo Image ◽

Image Model ◽

Geometric Invariants ◽

Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

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FREDHOLM DETERMINANT SOLUTION FOR NONLINEAR EQUATIONS ASSOCIATED WITH ISOSPECTRAL SCHRÖDINGER EIGENVALUE PROBLEM

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30132-2 ◽

1994 ◽

Vol 14 (4) ◽

pp. 426-437

Author(s):

Liede Huang ◽

Zhonghuan Xia

Keyword(s):

Eigenvalue Problem ◽

Nonlinear Equations ◽

Fredholm Determinant

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A comparative study of history-based versus vectorized Monte Carlo methods in the GPU/CUDA environment for a simple neutron eigenvalue problem

SNA + MC 2013 - Joint International Conference on Supercomputing in Nuclear Applications + Monte Carlo ◽

10.1051/snamc/201404206 ◽

2014 ◽

Cited By ~ 1

Author(s):

Tianyu Liu ◽

Xining Du ◽

Wei Ji ◽

X. George Xu ◽

Forrest B. Brown

Keyword(s):

Monte Carlo ◽

Eigenvalue Problem ◽

Comparative Study ◽

Monte Carlo Methods

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Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2006.11.1.14762 ◽

2006 ◽

Vol 11 (1) ◽

pp. 13-32 ◽

Cited By ~ 10

Author(s):

B. Bandyrskii ◽

I. Lazurchak ◽

V. Makarov ◽

M. Sapagovas

Keyword(s):

Differential Equation ◽

Eigenvalue Problem ◽

Variable Coefficient ◽

Order Differential Equation ◽

Integral Condition ◽

Second Order ◽

Computational Results ◽

Discrete Method ◽

Complex Eigenvalues ◽

Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

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