scholarly journals Numerical verification method for infinite dimensional eigenvalue problems

2009 ◽  
Vol 26 (2-3) ◽  
pp. 477-491 ◽  
Author(s):  
Kaori Nagatou
Keyword(s):  
Eigenvalue Problems ◽  
Numerical Verification ◽  
Verification Method ◽  
Infinite Dimensional

scholarly journals A note on the Ritz method with an application to overtone stellar pulsation theory

1968 ◽  
Vol 8 (2) ◽  
pp. 275-286 ◽  
Author(s):  
A. L. Andrew
Keyword(s):  
Numerical Solution ◽  
Eigenvalue Problems ◽  
Ritz Method ◽  
Linear Operators ◽  
Matrix Equations ◽  
Infinite Dimensional ◽  
Stellar Pulsation ◽  
Finite Matrix ◽  
The Matrix ◽  
Matrix Eigenvalue Problems

The Ritz method reduces eigenvalue problems involving linear operators on infinite dimensional spaces to finite matrix eigenvalue problems. This paper shows that for a certain class of linear operators it is possible to choose the coordinate functions so that numerical solution of the matrix equations is considerably simplified, especially when the matrices are large. The method is applied to the problem of overtone pulsations of stars.

Contact Dynamics of Reconfigurable Space Systems With Numerical Verification Method

2001 ◽  
Author(s):  
Takashi Takahashi ◽  
Saburo Matunaga
Keyword(s):  
Numerical Computation ◽  
Contact Dynamics ◽  
Numerical Verification ◽  
Space Systems ◽  
Guaranteed Accuracy ◽  
Experiment System ◽  
Verification Method ◽  
Satellite Systems ◽  
Cluster Satellite ◽  
The Difference

Abstract In order to analyze dynamics of space systems, such as cluster satellite systems and the capturing process of damaged satellites, it is necessary to consider such space systems as reconfigurable multibody systems. In this paper, we discuss the numerical computation of the dynamics of the ground experiment system to simulate the capturing and berthing process of a satellite by a dual-manipulator on the flat floor as an example. We have previously discussed the efficient dynamics algorithm for reconfigurable multibody system with topological changes. However, the contact dynamics, which is one of the most difficult issues in our study, remains to be discussed. We introduce two types of the linear complementarity problem (LCP) concerned with contact dynamics. The difference between the two types of LCP is whether impacts can be considered. Dynamic systems with impacts and friction are non-conservation systems; moreover the LCP is not always solvable. Therefore we must check if the solutions of the numerical computation are correct, or how accurate they are. In this paper, we derive the method of numerical computation with guaranteed accuracy of the LCP for contact dynamics.

scholarly journals LARGE N MATRIX MECHANICS ON THE LIGHT-CONE

2002 ◽  
Vol 17 (11) ◽  
pp. 1517-1542 ◽  
Author(s):  
M. B. HALPERN ◽  
CHARLES B. THORN
Keyword(s):  
Light Cone ◽  
Eigenvalue Problems ◽  
Hamiltonian Formulation ◽  
Cuntz Algebra ◽  
Conserved Quantities ◽  
Basic Tool ◽  
Dimensional Algebra ◽  
Infinite Dimensional ◽  
Matrix Mechanics ◽  
Large N

We report a simplification in the large N matrix mechanics of light-cone matrix field theories. The absence of pure creation or pure annihilation terms in the Hamiltonian formulation of these theories allows us to find their reduced large N Hamiltonians as explicit functions of the generators of the Cuntz algebra. This opens up a free-algebraic playground of new reduced models — all of which exhibit new hidden conserved quantities at large N and all of whose eigenvalue problems are surprisingly simple. The basic tool we develop for the study of these models is the infinite dimensional algebra of all normal-ordered products of Cuntz operators, and this algebra also leads us to a special number-conserving subset of these models, each of which exhibits an infinite number of new hidden conserved quantities at large N.

scholarly journals Numerical verification method for solutions of the perturbed Gelfand equation

2000 ◽  
Vol 7 (1) ◽  
pp. 251-262 ◽  
Author(s):  
Teruya Minamoto ◽  
Nobito Yamamoto ◽  
Mitsuhiro T. Nakao
Keyword(s):  
Numerical Verification ◽  
Verification Method
Sign in / Sign up

Export Citation Format

Share Document