Monthly Archives: November 2010

Sobol’s book from 1969

Recently a colleague forward me an email with a link to a scanned copy of Sobol’s book from 1969. The link is:

http://www.regmed.ru/getfile.asp?CatId=db&Name=IMSobol_1969_book.pdf The book can be cited using:

  • @preamble{
    “\def\cprime{$’$} ”
    }
    @book {Sobol1969,
    AUTHOR = {{{\cyr{T}}sobol{\cprime}, I. M.}},
    TITLE = {Mnogomernye kvadraturnye formuly i funktsii {K}haara},
    PUBLISHER = {Izdat. “Nauka”, Moscow},
    YEAR = {1969},
    PAGES = {288}
    }

The english translation of the book title is ‘Multidimensional quadrature formulae and Haar functions’.

Update 01/12/2010: Professor Sobol provided a response which is added at the end of this entry. Continue reading

QMC rules over R^s: Matlab code and numerical example

In this post you can find a Matlab code for constructing digital nets on \mathbb{R}^s which was recently proposed in J. Dick, Quasi-Monte Carlo numerical integration on \mathbb{R}^s: digital nets and worst-case error. Submitted, 2010. See the previous post where an explanation of the method and a link to the paper can be found. In the numerical example we consider a simple three-dimensional integral. In this example the computation time with the new method is reduced by a factor of ten and additionally the integration error is also reduced. The numerical result in the paper shows that, for the example considered there, that the computation time can be reduced from two and a half minutes to less than two seconds for a certain given error level. Continue reading