Removal of infinite eigenvalues in the generalized matrix eigenvalue problem

1989 ◽  
Vol 84 (1) ◽  
pp. 242-246 ◽  
Author(s):  
Dimitrios A. Goussis ◽  
Arne J. Pearlstein
Keyword(s):  
Eigenvalue Problem ◽  
Matrix Eigenvalue Problem ◽  
Matrix Eigenvalue ◽  
Generalized Matrix

A HIERARCHY OF HAMILTONIAN EQUATIONS ASSOCIATED WITH THE MODIFIED JAULENT–MIODEK HIERARCHY

2010 ◽  
Vol 24 (02) ◽  
pp. 183-193
Author(s):  
HAI-YONG DING ◽  
HONG-XIANG YANG ◽  
YE-PENG SUN ◽  
LI-LI ZHU
Keyword(s):  
Eigenvalue Problem ◽  
Evolution Equations ◽  
Trace Identity ◽  
Liouville Integrability ◽  
Matrix Eigenvalue Problem ◽  
Hamiltonian Structures ◽  
Hamiltonian Equations ◽  
Matrix Eigenvalue ◽  
Integrable Evolution

By considering a new four-by-four matrix eigenvalue problem, a hierarchy of Lax integrable evolution equations with four potentials is derived. The Hamiltonian structures of the resulting hierarchy are established by means of the generalized trace identity. The Liouville integrability for the hierarchy of the resulting Hamiltonian equations is presented.

A Matrix Eigenvalue Problem (G. Efroymson, A. Steger and S. Steinberg)

SIAM Review ◽  
1980 ◽  
Vol 22 (1) ◽  
pp. 99-100
Author(s):  
T. Sekiguchi ◽  
N. Kimura
Keyword(s):  
Eigenvalue Problem ◽  
Matrix Eigenvalue Problem ◽  
Matrix Eigenvalue

A FOUR-BY-FOUR MATRIX EIGENVALUE PROBLEM, RELATED HIERARCHY OF LAX INTEGRABLE EQUATIONS AND THEIR HAMILTONIAN STRUCTURES

2008 ◽  
Vol 22 (23) ◽  
pp. 4027-4040 ◽  
Author(s):  
XI-XIANG XU ◽  
HONG-XIANG YANG ◽  
WEI-LI CAO
Keyword(s):  
Eigenvalue Problem ◽  
Evolution Equations ◽  
Trace Identity ◽  
Liouville Integrability ◽  
Matrix Eigenvalue Problem ◽  
Hamiltonian Structures ◽  
Hamiltonian Equations ◽  
Integrable Equations ◽  
Matrix Eigenvalue ◽  
Integrable Evolution

Starting from a new four-by-four matrix eigenvalue problem, a hierarchy of Lax integrable evolution equations with four potentials is derived. The Hamiltonian structures of the resulting hierarchy are established by means of the generalized trace identity. The Liouville integrability for the hierarchy of the resulting Hamiltonian equations is proved.

Infinite Matrices, Ritz Theorem and Bound State Problems

1975 ◽  
Vol 30 (2) ◽  
pp. 256-261 ◽  
Author(s):  
A. K. Mitra
Keyword(s):  
Eigenvalue Problem ◽  
Convenient Method ◽  
Bound State ◽  
Wave Functions ◽  
Infinite Matrix ◽  
Variational Technique ◽  
Matrix Eigenvalue Problem ◽  
Schroedinger Operator ◽  
Matrix Eigenvalue ◽  
Finite Matrix

Abstract The straight forward application of the Ritz variational technique has been shown to be a very convenient method for obtaining numerically the first few discrete eigenvalues of the Schroedinger operator with certain special types of potentials. This method solves essentially the (finite) matrix eigenvalue problem obtained by truncating the infinite matrix representing the Schroedinger operator with respect to the Coulomb wave functions. The Ritz theorem justifies the validity of this truncation procedure.

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