Riemannian Newton Method for the Multivariate Eigenvalue Problem

2010 ◽  
Vol 31 (5) ◽  
pp. 2972-2996 ◽  
Author(s):  
Lei-Hong Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Newton Method ◽  
Multivariate Eigenvalue Problem

Symbolic Newton method for two-parameter eigenvalue problem

1997 ◽  
Vol 31 (3) ◽  
pp. 36
Author(s):  
Michio Sakakihara ◽  
Shigekazu Nakagawa
Keyword(s):  
Eigenvalue Problem ◽  
Newton Method ◽  
Two Parameter

Sensitivity analysis for the multivariate eigenvalue problem

2013 ◽  
Vol 26 ◽  
Author(s):  
Xin-guo Liu ◽  
Wei-guo Wang ◽  
Lian-hua Xu
Keyword(s):  
Sensitivity Analysis ◽  
Eigenvalue Problem ◽  
Multivariate Eigenvalue Problem

The Projected Newton Method Has Order $1 + \sqrt 2 $ for the Symmetric Eigenvalue Problem

1988 ◽  
Vol 25 (6) ◽  
pp. 1376-1382 ◽  
Author(s):  
R. A. Tapia ◽  
David L. Whitley
Keyword(s):  
Eigenvalue Problem ◽  
Newton Method ◽  
Symmetric Eigenvalue Problem ◽  
Projected Newton Method

On a Multivariate Eigenvalue Problem, Part I: Algebraic Theory and a Power Method

1993 ◽  
Vol 14 (5) ◽  
pp. 1089-1106 ◽  
Author(s):  
Moody T. Chu ◽  
J. Loren Watterson
Keyword(s):  
Eigenvalue Problem ◽  
Algebraic Theory ◽  
Power Method ◽  
Multivariate Eigenvalue Problem

On the scaled newton method for the symmetric eigenvalue problem

Computing ◽  
1990 ◽  
Vol 45 (3) ◽  
pp. 277-282 ◽  
Author(s):  
S. M. Grzegórski
Keyword(s):  
Eigenvalue Problem ◽  
Newton Method ◽  
Symmetric Eigenvalue Problem

scholarly journals Block Preconditioning Matrices for the Newton Method to Compute the Dominant λ-Modes Associated with the Neutron Diffusion Equation

2019 ◽  
Vol 24 (1) ◽  
pp. 9
Author(s):  
Amanda Carreño ◽  
Luca Bergamaschi ◽  
Angeles Martinez ◽  
Antoni Vidal-Ferrándiz ◽  
Damian Ginestar ◽  
...  
Keyword(s):  
Eigenvalue Problem ◽  
Diffusion Equation ◽  
Newton Method ◽  
Computational Time ◽  
Neutron Diffusion ◽  
The Matrix ◽  
Generalized Newton ◽  
Block Preconditioners ◽  
Matrix Free ◽  
Neutron Diffusion Equation

In nuclear engineering, the λ -modes associated with the neutron diffusion equation are applied to study the criticality of reactors and to develop modal methods for the transient analysis. The differential eigenvalue problem that needs to be solved is discretized using a finite element method, obtaining a generalized algebraic eigenvalue problem whose associated matrices are large and sparse. Then, efficient methods are needed to solve this problem. In this work, we used a block generalized Newton method implemented with a matrix-free technique that does not store all matrices explicitly. This technique reduces mainly the computational memory and, in some cases, when the assembly of the matrices is an expensive task, the computational time. The main problem is that the block Newton method requires solving linear systems, which need to be preconditioned. The construction of preconditioners such as ILU or ICC based on a fully-assembled matrix is not efficient in terms of the memory with the matrix-free implementation. As an alternative, several block preconditioners are studied that only save a few block matrices in comparison with the full problem. To test the performance of these methodologies, different reactor problems are studied.

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

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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