Some Non Standard Applications of the Laplace Method

2014 ◽  
pp. 41-47
Author(s):  
Calixto P. Calderón ◽  
Wilfredo O. Urbina
Keyword(s):  
Laplace Method

scholarly journals Precision Annealing Monte Carlo Methods for Statistical Data Assimilation: Metropolis-Hastings Procedures

2019 ◽  
Author(s):  
Adrian S. Wong ◽  
Kangbo Hao ◽  
Zheng Fang ◽  
Henry D. I. Abarbanel
Keyword(s):  
Monte Carlo ◽  
Probability Distribution ◽  
Data Assimilation ◽  
Conditional Probability ◽  
Information Transfer ◽  
Statistical Data ◽  
Laplace Method ◽  
Conditional Probability Distribution ◽  
Expected Values ◽  
Transfer Of Information

Abstract. Statistical Data Assimilation (SDA) is the transfer of information from field or laboratory observations to a user selected model of the dynamical system producing those observations. The data is noisy and the model has errors; the information transfer addresses properties of the conditional probability distribution of the states of the model conditioned on the observations. The quantities of interest in SDA are the conditional expected values of functions of the model state, and these require the approximate evaluation of high dimensional integrals. We introduce a conditional probability distribution and use the Laplace method with annealing to identify the maxima of the conditional probability distribution. The annealing method slowly increases the precision term of the model as it enters the Laplace method. In this paper, we extend the idea of precision annealing (PA) to Monte Carlo calculations of conditional expected values using Metropolis-Hastings methods.

An assessment of the Padé-Laplace method for transient electric birefringence decay analysis

1992 ◽  
Vol 16 (3) ◽  
pp. 249-259 ◽  
Author(s):  
John S. Bowers ◽  
Robert K. Prud'homme ◽  
Raymond S. Farinato
Keyword(s):  
Laplace Method ◽  
Electric Birefringence ◽  
Transient Electric Birefringence

scholarly journals Cluster analysis of European Y-chromosomal STR haplotypes using the discrete Laplace method

2014 ◽  
Vol 11 ◽  
pp. 182-194 ◽  
Author(s):  
Mikkel Meyer Andersen ◽  
Poul Svante Eriksen ◽  
Niels Morling
Keyword(s):  
Cluster Analysis ◽  
Laplace Method

scholarly journals External version of Laplace method

2014 ◽  
Vol 9 ◽  
pp. 1223-1228
Author(s):  
Tahir H. Ismail
Keyword(s):  
Laplace Method ◽  
External Version

scholarly journals Extensions of the Laplace method

1954 ◽  
Vol 5 (4) ◽  
pp. 526-526
Author(s):  
D. L. Thomsen
Keyword(s):  
Laplace Method

scholarly journals Numerical calculation for coupling vibration system by Piecewise-Laplace method

2020 ◽  
Vol 103 (3) ◽  
pp. 003685042093855
Author(s):  
Pan Fang ◽  
Kexin Wang ◽  
Liming Dai ◽  
Chixiang Zhang
Keyword(s):  
Numerical Computation ◽  
Laplace Transformation ◽  
Original System ◽  
Continuity Condition ◽  
Kutta Method ◽  
Laplace Method ◽  
Time Step ◽  
Coupling Vibration ◽  
Runge Kutta Method ◽  
Runge Kutta

To improve the reliability and accuracy of dynamic machine in design process, high precision and efficiency of numerical computation is essential means to identify dynamic characteristics of mechanical system. In this paper, a new computation approach is introduced to improve accuracy and efficiency of computation for coupling vibrating system. The proposed method is a combination of piecewise constant method and Laplace transformation, which is simply called as Piecewise-Laplace method. In the solving process of the proposed method, the dynamic system is first sliced by a series of continuous segments to reserve physical attribute of the original system; Laplace transformation is employed to separate coupling variables in segment system, and solutions of system in complex domain can be determined; then, considering reverse Laplace transformation and residues theorem, solution in time domain can be obtained; finally, semi-analytical solution of system is given based on continuity condition. Through comparison of numerical computation, it can be found that precision and efficiency of numerical results with the Piecewise-Laplace method is better than Runge-Kutta method within same time step. If a high-accuracy solution is required, the Piecewise-Laplace method is more suitable than Runge-Kutta method.

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