Overview
Write a short report about Monte Carlo integration methods. Two short introductions are provided in the articles
Monte Carlo and quasi-Monte Carlo methods (Links to an external site.) Section 1,2 (You don’t need to include arguments based on the central limit theorem). High-dimensional integration: The quasi-Monte Carlo way (Links to an external site.) Sections 1, 2.1, 2.2.
Save your time - order a paper!
Get your paper written from scratch within the tight deadline. Our service is a reliable solution to all your troubles. Place an order on any task and we will take care of it. You won’t have to worry about the quality and deadlines
Order Paper NowYou may need more information, which can be found on the internet, journal articles and book chapters. The latter may be available online e.g. in the UCF Library or Google Books.
Your report should contain a description of the methods, some arguments/proofs why they work and some numerical experiments in Python. In particular, discuss the following two questions:
How does Monte Carlo integration compare to Newton Cotes formals or Gauss quadrature? How does Monte Carlo and Newton Cotes/Gauss quadrature behave in high dimensions?
For comparison, include a description of Newton Cotes or Gauss quadrature in multiple dimensions. Convergence theory can be cited.
Organization:
Aim for no more than five pages. The goal is not to squeeze in as many facts as possible but to write down the important arguments and results in a clear and concise way. You may use literature beyond the two given papers above. Citations in your report must be from acceptable scientific sources. These include journal articles, books and arXiv.org (Links to an external site.) but not Wikipedia, blogs, etc.. Many authors make their publications freely available online, the UCF library has many journals/books online and Google Books often allows you to see the relevant pages
