scholarly journals Monte Carlo Methods and the Koksma-Hlawka Inequality

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 725
Author(s):  
Sergey Ermakov ◽  
Svetlana Leora
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Random Processes ◽  
Random Numbers ◽  
Average Order ◽  
New Approach ◽  
Average Value ◽  
Acceptable Accuracy ◽  
Cubature Formulas ◽  
The Monte Carlo Method

The solution of a wide class of applied problems can be represented as an integral over the trajectories of a random process. The process is usually modeled with the Monte Carlo method and the integral is estimated as the average value of a certain function on the trajectories of this process. Solving this problem with acceptable accuracy usually requires modeling a very large number of trajectories; therefore development of methods to improve the accuracy of such algorithms is extremely important. The paper discusses Monte Carlo method modifications that use some classical results of the theory of cubature formulas (quasi-random methods). A new approach to the derivation of the well known Koksma-Hlawka inequality is pointed out. It is shown that for high ( s > 5 ) dimensions of the integral, the asymptotic decrease of the error comparable to the asymptotic behavior of the Monte Carlo method, can be achieved only for a very large number of nodes N. It is shown that a special criterion can serve as a correct characteristic of the error decrease (average order of the error decrease). Using this criterion, it is possible to analyze the error for reasonable values of N and to compare various quasi-random sequences. Several numerical examples are given. Obtained results make it possible to formulate recommendations on the correct use of the quasi-random numbers when calculating integrals over the trajectories of random processes.

scholarly journals Prediksi Tingkat Penerimaan Lulusan Siswa Kejuruan dalam Dunia Usaha dan Industri Menggunakan Metode Monte Carlo

2020 ◽  
pp. 84-89
Author(s):  
Hasanatul Iftitah ◽  
Y Yuhandri
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Probability Distribution ◽  
Prediction Accuracy ◽  
Vocational School ◽  
Vocational Schools ◽  
Random Numbers ◽  
Vocational High School ◽  
The Monte Carlo Method ◽  
Academic Year

Vocational High School (SMK) Negeri 4 Kota Jambi is one of the favorite vocational schools in Jambi City which is also the only pure tourism vocational school in Jambi Province. SMK Negeri 4 Kota Jambi has several vocational majors, namely culinary, beauty, fashion and hospitality. In general, students who choose to attend vocational schools have the hope of being able to work immediately after graduating from school, they do not need to continue to study to be able to work. In this study, researchers will predict the level of acceptance of students from SMK Negeri 4 Kota Jambi in the business and industrial world using the Monte Carlo method. Monte Carlo is a method that can find values ​​that are close to the actual value of events that will occur based on the distribution of sampling data. The technique of this method is to select random numbers from the probability distribution to perform the simulation. The data used in this study is the data of students from SMK Negeri 4 Kota Jambi who worked from the 2015/2016 Academic Year to the 2018/2019 Academic Year. Furthermore, the data will be processed using the Monte Carlo method. The simulation will be implemented using PHP programming. The result of this research is the level of prediction accuracy of students of SMK Negeri 4 Kota Jambi who are accepted in the business and industrial world using the Monte Carlo method is 84%.

scholarly journals Monte Carlo Simulation of the Echo Signals from Low-Flying Targets for Airborne Radar

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mingyuan Man ◽  
Zhenya Lei ◽  
Yongjun Xie ◽  
Botao Chen ◽  
Qing Wang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Half Space ◽  
Ground Surface ◽  
Physical Optics ◽  
Airborne Radar ◽  
Average Value ◽  
The Monte Carlo Method ◽  
Multipath Effects ◽  
Actual Environment

A demonstrated hybrid method based on the combination of half-space physical optics method (PO), graphical-electromagnetic computing (GRECO), and Monte Carlo method on echo signals from low-flying targets based on actual environment for airborne radar is presented in this paper. The half-space physical optics method , combined with the graphical-electromagnetic computing (GRECO) method to eliminate the shadow regions quickly and rebuild the target automatically, is employed to calculate the radar cross section (RCS) of the conductive targets in half space fast and accurately. The direct echo is computed based on the radar equation. The reflected paths from sea or ground surface cause multipath effects. In order to accurately obtain the echo signals, the phase factors are modified for fluctuations in multipath, and the statistical average value of the echo signals is obtained using the Monte Carlo method. A typical simulation is performed, and the numerical results show the accuracy of the proposed method.

Independent and Dependent Scattering for Semitransparent Media Containing Bubbles

2004 ◽  
Author(s):  
Jaona H. Randrianalisoa ◽  
Dominique Baillis
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Bubble Size ◽  
Volume Fraction ◽  
Geometric Optic ◽  
New Approach ◽  
The Monte Carlo Method ◽  
Spherical Bubbles ◽  
Optic Limit ◽  
Radiative Characteristics

The objective of this present work is to provide a new approach for the radiative characteristics computation of semitransparent media containing spherical bubbles. The bubble size is considred much larger than the wavelength. First, previous models from the literature based on the independent theory are reviewed and established in the Geometric optic limit. Second, a predictive model using the Monte Carlo method is developed. The results obtained from the independent theory models and the Monte Carlo approach are compared. In addition, by varying the bubbles volume fraction, we investigate the limit of validity of the independent theory in such medium.

scholarly journals A Hybrid Method for Evaluating of Lightning Performance of Overhead Lines based on Monte Carlo Procedure

2016 ◽  
Vol 67 (4) ◽  
pp. 246-252
Author(s):  
Reza Shariatinasab ◽  
Pooya Tadayon ◽  
Akihiro Ametani
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Risk Analysis ◽  
Hybrid Method ◽  
Overhead Lines ◽  
Monte Carlo Procedure ◽  
Acceptable Accuracy ◽  
The Monte Carlo Method ◽  
Analytical Relations

Abstract This paper proposes a hybrid method for calculating lightning performance of overhead lines caused by direct strokes by combining Lattice diagram together with the Monte Carlo method. In order to go through this, firstly, the proper analytical relations for overvoltages calculation are established based on Lattice diagram. Then, the Monte Carlo procedure is applied to the obtained analytical relations. The aim of the presented method that will be called ‘ML method’ is simply estimation of the lightning performance of the overhead lines and performing the risk analysis of power apparatus with retaining the acceptable accuracy. To confirm the accuracy, the calculated results of the presented ML method are compared with those calculated by the EMTP/ATP simulation.

Geometric Synthesis of Manipulators Using the Monte Carlo Method

1990 ◽  
Vol 112 (3) ◽  
pp. 450-452 ◽  
Author(s):  
J. Rastegar ◽  
B. Fardanesh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Installation Space ◽  
Joint Motion ◽  
Task Space ◽  
Arbitrary Geometry ◽  
New Approach ◽  
Space Geometry ◽  
The Monte Carlo Method

A new approach to the solution of problems of geometric synthesis of manipulators is presented. It utilizes the Monte Carlo method, is general, and can be applied to any type of manipulator. Joint motion limitations can be included. The task space may have any arbitrary geometry. The allowable manipulator installation space is determined. Synthesis for a specified number of possible configurations (branches), and optimization of task space geometry are discussed.

Sign in / Sign up

Export Citation Format

Share Document