On the Global Convergence of the Toda Lattice for Real Normal Matrices and Its Applications to the Eigenvalue Problem

1984 ◽  
Vol 15 (1) ◽  
pp. 98-104 ◽  
Author(s):  
Moody T. Chu
Keyword(s):  
Global Convergence ◽  
Eigenvalue Problem ◽  
Toda Lattice ◽  
Normal Matrices

scholarly journals A New Jacobian-Like Method for the Polyhedral Cone-Constrained Eigenvalue Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Guo Sun
Keyword(s):  
Global Convergence ◽  
Eigenvalue Problem ◽  
Numerical Experiments ◽  
Quadratic Convergence ◽  
Polyhedral Cone ◽  
System Of Equations ◽  
Local Quadratic Convergence ◽  
Ncp Function

The eigenvalue problem over a polyhedral cone is studied in this paper. Based on the F-B NCP function, we reformulate this problem as a system of equations and propose a Jacobian-like method. The global convergence and local quadratic convergence of the proposed method are established under suitable assumptions. Preliminary numerical experiments for a special polyhedral cone are reported in this paper to show the validity of the proposed method.

scholarly journals Exceptional points, non-normal matrices, hierarchy of spin matrices and an eigenvalue problem

2014 ◽  
Vol 25 (11) ◽  
pp. 1450059 ◽  
Author(s):  
Willi-Hans Steeb ◽  
Yorick Hardy
Keyword(s):  
Eigenvalue Problem ◽  
Hilbert Spaces ◽  
Linear Operators ◽  
Normal Matrices ◽  
Exceptional Points ◽  
Finite Dimensional

Exceptional points of a class of non-hermitian Hamilton operators Ĥ of the form Ĥ = Ĥ0+ iĤ1are studied, where Ĥ0and Ĥ1are hermitian operators. Finite dimensional Hilbert spaces are considered. The linear operators Ĥ0and Ĥ1are given by spin matrices for spin s = 1/2, 1, 3/2, …. Since the linear operators studied are non-normal, properties of such operators are described.

scholarly journals Analysis of the convergence properties of Rubenstein's method for the determination of the lower modes of vibration of a multi-degree of freedom system

1964 ◽  
Vol 54 (6A) ◽  
pp. 1757-1766
Author(s):  
M. E. J. O'Kelly
Keyword(s):  
Global Convergence ◽  
Eigenvalue Problem ◽  
Degree Of Freedom ◽  
Convergence Properties ◽  
Modes Of Vibration

abstract This paper analyzes the convergence properties of a method, recently proposed by Rubenstein, for the determination of the lower modes of vibration of a multi-degree of freedom system from a reduced eigenvalue problem. It is shown that under certain conditions the method converges to the exact eigenvalues. It does not have global convergence and hence some care must be exercised when using it.

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