Calculation of partial widths and isotope effects for reactive resonances by a reaction‐path Hamiltonian model: Test against accurate quantal results for a twin‐saddle point system

1984 ◽  
Vol 80 (8) ◽  
pp. 3569-3573 ◽  
Author(s):  
Rex T. Skodje ◽  
David W. Schwenke ◽  
Donald G. Truhlar ◽  
Bruce C. Garrett
Keyword(s):  
Saddle Point ◽  
Model Test ◽  
Reaction Path ◽  
Isotope Effects ◽  
Point System ◽  
Hamiltonian Model ◽  
Saddle Point System ◽  
Reaction Path Hamiltonian

Quantum Hall effect in a saddle-point system

1998 ◽  
Vol 2 (1-4) ◽  
pp. 523-526
Author(s):  
M.V Budantsev ◽  
Z.D Kvon ◽  
A.G Pogosov ◽  
E.B Olshanetskii ◽  
D.K Maude ◽  
...  
Keyword(s):  
Saddle Point ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Point System ◽  
Saddle Point System

An Iterative Two-Grid Method of A Finite Element PML Approximation for the Two Dimensional Maxwell Problem

2012 ◽  
Vol 4 (2) ◽  
pp. 175-189
Author(s):  
Chunmei Liu ◽  
Shi Shu ◽  
Yunqing Huang ◽  
Liuqiang Zhong ◽  
Junxian Wang
Keyword(s):  
Finite Element ◽  
Saddle Point ◽  
Grid Method ◽  
Variational Problems ◽  
Auxiliary System ◽  
Point System ◽  
Saddle Point System ◽  
System 2 ◽  
System 1 ◽  
Coarse Space

AbstractIn this paper, we propose an iterative two-grid method for the edge finite element discretizations (a saddle-point system) of Perfectly Matched Layer(PML) equations to the Maxwell scattering problem in two dimensions. Firstly, we use a fine space to solve a discrete saddle-point system of H(grad) variational problems, denoted by auxiliary system 1. Secondly, we use a coarse space to solve the original saddle-point system. Then, we use a fine space again to solve a discrete H(curl)-elliptic variational problems, denoted by auxiliary system 2. Furthermore, we develop a regularization diagonal block preconditioner for auxiliary system 1 and use H-X preconditioner for auxiliary system 2. Hence we essentially transform the original problem in a fine space to a corresponding (but much smaller) problem on a coarse space, due to the fact that the above two preconditioners are efficient and stable. Compared with some existing iterative methods for solving saddle-point systems, such as PMinres, numerical experiments show the competitive performance of our iterative two-grid method.

scholarly journals Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Ling Jian ◽  
Shuqian Shen ◽  
Yunquan Song
Keyword(s):  
Blast Furnace ◽  
Support Vector Machines ◽  
Saddle Point ◽  
Least Squares ◽  
Null Space ◽  
Support Vector ◽  
Point System ◽  
Trend Prediction ◽  
Vector Machines ◽  
Saddle Point System

The solution of least squares support vector machines (LS-SVMs) is characterized by a specific linear system, that is, a saddle point system. Approaches for its numerical solutions such as conjugate methods Sykens and Vandewalle (1999) and null space methods Chu et al. (2005) have been proposed. To speed up the solution of LS-SVM, this paper employs the minimal residual (MINRES) method to solve the above saddle point system directly. Theoretical analysis indicates that the MINRES method is more efficient than the conjugate gradient method and the null space method for solving the saddle point system. Experiments on benchmark data sets show that compared with mainstream algorithms for LS-SVM, the proposed approach significantly reduces the training time and keeps comparable accuracy. To heel, the LS-SVM based on MINRES method is used to track a practical problem originated from blast furnace iron-making process: changing trend prediction of silicon content in hot metal. The MINRES method-based LS-SVM can effectively perform feature reduction and model selection simultaneously, so it is a practical tool for the silicon trend prediction task.

New homogenization method for diffusion equations

2018 ◽  
Vol 33 (2) ◽  
pp. 85-93 ◽  
Author(s):  
Yuri A. Kuznetsov
Keyword(s):  
Saddle Point ◽  
Diffusion Coefficients ◽  
Diffusion Problem ◽  
Homogenization Method ◽  
Diffusion Equations ◽  
Point System ◽  
Algebraic Problem ◽  
Saddle Point System ◽  
Saddle Point Matrix ◽  
Diffusion Problems

Abstract In this paper, we propose and investigate a new homogenization method for diffusion problems in domains with multiple inclusions with large values of diffusion coefficients. The diffusion problem is approximated by the P1-finite element method on a triangular mesh. The underlying algebraic problem is replaced by a special system with a saddle point matrix. For the solution of the saddle point system we use the typical asymptotic expansion. We prove the error estimates and convergence of the expanded solutions. Numerical results confirm the theoretical conclusions.

On evaluating the reaction path Hamiltonian

1988 ◽  
Vol 88 (2) ◽  
pp. 922-935 ◽  
Author(s):  
Michael Page ◽  
James W. McIver
Keyword(s):  
Reaction Path ◽  
Reaction Path Hamiltonian
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