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Monte Carlo and quasi-Monte Carlo methods
Acta Numerica, 1998Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N−1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction ...
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Analysis of a Monte-Carlo Nystrom Method
SIAM Journal on Numerical Analysis, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Florian Feppon, Habib Ammari
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The 13th international conference on laser interactions and related plasma phenomena, 1997
Monte Carlo methods appropriate to simulate the transport of x-rays, neutrons, ions and electrons in Inertial Confinement Fusion targets are described and analyzed. The Implicit Monte Carlo method of x-ray transport handles symmetry within indirect drive ICF hohlraums well, but can be improved 50X in efficiency by angular biasing the x-rays towards the
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Monte Carlo methods appropriate to simulate the transport of x-rays, neutrons, ions and electrons in Inertial Confinement Fusion targets are described and analyzed. The Implicit Monte Carlo method of x-ray transport handles symmetry within indirect drive ICF hohlraums well, but can be improved 50X in efficiency by angular biasing the x-rays towards the
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1987
The term ‘Monte Carlo methods’ is used to refer to two different, though closely related, techniques. The first meaning, currently the less common one among economists, is the evaluation of definite integrals by use of random variables. The idea is to evaluate \(\int_a^b {F\left( x \right)} {\text{d}}x\) where x may be a vector) by estimating \(\int_a ...
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The term ‘Monte Carlo methods’ is used to refer to two different, though closely related, techniques. The first meaning, currently the less common one among economists, is the evaluation of definite integrals by use of random variables. The idea is to evaluate \(\int_a^b {F\left( x \right)} {\text{d}}x\) where x may be a vector) by estimating \(\int_a ...
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A monte carlo method for factorization
BIT, 1975The following simple method will find small prime factors \(p\) of a number \(n\) in \(O(p^{1/2})\) arithmetical operations as opposed to the \(O(p)\) operations required by trial division. Let \(x_0=2\), \(x_{i+1}\equiv x_i^2-1\pmod n\) (other similar sequences may be used). Generate in turn the pairs \((x_j,x_{2j})\), accumulating the product \(\pmod
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Optimization by Monte Carlo Methods
2009It may be that the problem of optimization entails more time and effort by mankind than any other mathematical problem. For example, it permeates nearly all design and engineering projects.
Ronald W. Shonkwiler, Franklin Mendivil
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Reliability Engineering & System Safety, 2010
To reduce cost of Monte Carlo (MC) simulations for time-consuming processes, Bayesian Monte Carlo (BMC) is introduced in this paper. The BMC method reduces number of realizations in MC according to the desired accuracy level. BMC also provides a possibility of considering more priors. In other words, different priors can be integrated into one model by
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To reduce cost of Monte Carlo (MC) simulations for time-consuming processes, Bayesian Monte Carlo (BMC) is introduced in this paper. The BMC method reduces number of realizations in MC according to the desired accuracy level. BMC also provides a possibility of considering more priors. In other words, different priors can be integrated into one model by
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2019
The sequential use of random numbers, to sample the values of probability variables, allows obtaining solutions to mathematical problems such as the Monte Carlo method, that allows to model stochastic parameters or deterministic based on random sampling.
Lorenzo Cevallos-Torres +1 more
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The sequential use of random numbers, to sample the values of probability variables, allows obtaining solutions to mathematical problems such as the Monte Carlo method, that allows to model stochastic parameters or deterministic based on random sampling.
Lorenzo Cevallos-Torres +1 more
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Monte Carlo and Quasi-Monte Carlo Methods 2006
2008This book represents the refereed proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, held in Ulm (Germany) in August 2006. The proceedings include carefully selected papers on many aspects of Monte Carlo and quasi-Monte Carlo methods and their applications, as well as providing ...
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