A Parallel Jacobi-Davidson Algorithm with Block FSAI Preconditioning

2011 ◽  
Author(s):  
M. Ferronato ◽  
C. Janna ◽  
G. Pini ◽  
G. Gambolati ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Davidson Algorithm

Mesh independence of the generalized Davidson algorithm

2020 ◽  
Vol 409 ◽  
pp. 109322
Author(s):  
C.T. Kelley ◽  
J. Bernholc ◽  
E.L. Briggs ◽  
Steven Hamilton ◽  
Lin Lin ◽  
...  
Keyword(s):  
Mesh Independence ◽  
Davidson Algorithm

CALCULATION OF SELECTED HIGHLY EXCITED VIBRATIONAL STATES OF POLYATOMIC MOLECULES BY THE DAVIDSON ALGORITHM

2003 ◽  
Vol 02 (04) ◽  
pp. 609-620 ◽  
Author(s):  
FABIENNE RIBEIRO ◽  
CHRISTOPHE IUNG ◽  
CLAUDE LEFORESTIER
Keyword(s):  
Energy Levels ◽  
Normal Modes ◽  
Chem Phys ◽  
Polyatomic Molecules ◽  
Zero Order ◽  
Basis Set ◽  
Vibrational States ◽  
Diagonalization Method ◽  
Davidson Algorithm ◽  
High Overtone

We described an improved version of a modified Davidson scheme previously introduced (F. Ribeiro, C. Iung and C. Leforestier, Chem. Phys. Lett.362, 199 (2002)), aimed at computing highly excited energy levels of polyatomic molecules. The key ingredient is a prediagonalization-perturbation step performed on a subspace of a curvilinear normal modes basis set (including diagonal anharmonicities). The efficiency of the method is demonstrated by computing the lowest 350 vibrational states of A′ symmetry of the HFCO molecule. Also shown is the possibility to restrict the calculation to selected energy levels, based on their zero-order description. This State Filtered Diagonalization method is illustrated on a high overtone (7ν5) of the OCF bend, and on the few energy levels (20) which have been experimentally assigned up to 5000 cm -1 of excitation energy.

Calculating Flux Perturbations with a Davidson Algorithm

1999 ◽  
Vol 131 (3) ◽  
pp. 370-386
Author(s):  
Chung-Hsing Hu ◽  
Wen-Wei Lin ◽  
Yen-Wan Hsueh Liu
Keyword(s):  
Davidson Algorithm

A GRAPH BASED DAVIDSON ALGORITHM FOR THE GRAPH PARTITIONING PROBLEM

1999 ◽  
Vol 10 (02) ◽  
pp. 225-246 ◽  
Author(s):  
MICHAEL HOLZRICHTER ◽  
SUELY OLIVEIRA
Keyword(s):  
Graph Theory ◽  
Load Balancing ◽  
Graph Partitioning ◽  
Graph Laplacian ◽  
Matrix Factorizations ◽  
Graph Partitioning Problem ◽  
Spectral Graph ◽  
Partitioning Problem ◽  
Davidson Algorithm ◽  
Spectral Graph Partitioning

The problem of partitioning a graph such that the number of edges incident to vertices in different partitions is minimized, arises in many contexts. Some examples include its recursive application for minimizing fill-in in matrix factorizations and load-balancing for parallel algorithms. Spectral graph partitioning algorithms partition a graph using the eigenvector associated with the second smallest eigenvalue of a matrix called the graph Laplacian. The focus of this paper is the use graph theory to compute this eigenvector more quickly.

Understanding draws in Elo rating algorithm

2020 ◽  
Vol 16 (3) ◽  
pp. 211-220
Author(s):  
Leszek Szczecinski ◽  
Aymen Djebbi
Keyword(s):  
Loss Probability ◽  
The Other ◽  
Premier League ◽  
Other Hand ◽  
Davidson Algorithm ◽  
English Premier League ◽  
Binary Games

AbstractThis work is concerned with the interpretation of the results produced by the well known Elo algorithm applied in various sport ratings. The interpretation consists in defining the probabilities of the game outcomes conditioned on the ratings of the players and should be based on the probabilistic rating-outcome model. Such a model is known in the binary games (win/loss), allowing us to interpret the rating results in terms of the win/loss probability. On the other hand, the model for the ternary outcomes (win/loss/draw) has not been yet shown even if the Elo algorithm has been used in ternary games from the very moment it was devised. Using the draw model proposed by Davidson in 1970, we derive a new Elo-Davidson algorithm, and show that the Elo algorithm is its particular instance. The parameters of the Elo-Davidson are then related to the frequency of draws which indicates that the Elo algorithm silently assumes games with 50% of draws. To remove this assumption, often unrealistic, the Elo-Davidson algorithm should be used as it improves the fit to the data. The behaviour of the algorithms is illustrated using the results from English Premier League.

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