scholarly journals A New Method for Solving an Eigenvalue Problem for a System of Three Coulomb Particles within the Hyperspherical Adiabatic Representation

2000 ◽  
Vol 163 (2) ◽  
pp. 328-348 ◽  
Author(s):  
A.G. Abrashkevich ◽  
M.S. Kaschiev ◽  
S.I. Vinitsky
Keyword(s):  
Eigenvalue Problem ◽  
New Method ◽  
Adiabatic Representation ◽  
Hyperspherical Adiabatic

NEW METHOD FOR SCHRÖDINGER EIGENVALUE PROBLEM — The Case of the Potential V(x) = 2μx2 + λx4

2012 ◽  
Vol 17 ◽  
pp. 149-158
Author(s):  
TORU NAKAMURA ◽  
HIROSHI EZAWA ◽  
KEIJI WATANABE ◽  
TOSHIHARU IRISAWA
Keyword(s):  
Eigenvalue Problem ◽  
Iteration Procedure ◽  
Divergent Series ◽  
New Method ◽  
Wkb Method ◽  
Quartic Potential

A new method is proposed to solve the Schrödinger eigenvalue problem. Remarkably the iteration procedure is found to be convergent in the case of the quartic potential for which the perturbation and the WKB method are known to give divergent series.

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.

P-SS Algorithm for Solving the Eigenvalue Problem of Finite Element System

2013 ◽  
Vol 300-301 ◽  
pp. 1118-1121
Author(s):  
Jie Fang Wang ◽  
Wei Guang An
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
New Method ◽  
Power Method ◽  
Small System ◽  
Element System ◽  
Shrinkage Method

P-SS algorithm for solving eigenvalue problem was obtained, based on the power method and the similar shrinkage method. This algorithm can be used to not only solve all eigenvalues of small system, but also partial eigenvalues of large finite element system. The calculation program of this algorithm is universal and practical. Compared with the existing methods, the error of P-SS method is very small, and it signify that the new method is feasible and convenient.

scholarly journals Towards a Method for the Accurate Solution of the Schrödinger Wave Equation in Many Variables. I. Formulation of the Method for an Eigenvalue Problem without Symmetry Conditions

1959 ◽  
Vol 12 (4) ◽  
pp. 430
Author(s):  
IM Bassett
Keyword(s):  
Wave Equation ◽  
Eigenvalue Problem ◽  
Digital Computer ◽  
Accurate Solution ◽  
New Method ◽  
Electronic Digital Computer

The aim of this paper and those following is to formulate and explore a new method, suitable for use with an electronic digital computer, for the solution of eigenvalue. eigenfunction problems in many variables, with the aim of applying the method to the Schrodinger wave equation.

A New Method for the Eigenvalue Problem of Structures with Uncertain-but-Non-Random Parameters

2013 ◽  
Vol 300-301 ◽  
pp. 765-770
Author(s):  
Jie Jie Zhang ◽  
Bo Fang ◽  
Li Jun Tan ◽  
Wen Hu Huang ◽  
Tao Lin
Keyword(s):  
Eigenvalue Problem ◽  
Dynamical Theory ◽  
The Other ◽  
New Method ◽  
Upper And Lower Bounds ◽  
Matrix Inequality ◽  
Random Parameters ◽  
Numerical Examples ◽  
Inequality Theory ◽  
Dynamical Parameters

In this paper, the eigenvalue problem that involves uncertain-but-non-random parameters is discussed. The error of dynamical parameters of a system is unavoidable in the course of manufacture and installation. Eigenvalues of the system are hard to obtain by the traditional dynamical theory. A new method based on matrix inequality theory is developed to evaluate the upper and lower bounds of the eigenvalues. In this method, properties of matrix’s spectral radius and norm are used. The illustrative numerical examples are provided to demonstrate the validity of the method. Compared with the other methods, the calculated results show that the proposed method in this paper is effective in evaluating bounds of the eigenvalues of structures with uncertain-but-bounded parameters.

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