THE WWW VIRTUAL LIBRARY:
RANDOM NUMBERS and MONTE CARLO METHODS

QUASI MONTE CARLO METHODS

In addition to our links on Random Number Generation and Monte Carlo Methods we also provide some Web-sites on Quasi-Monte Carlo Methods. Quasi-Monte Carlo methods deal with highly uniform point sets in high dimensions. They have become a most helpful technique to solve simulation problems, for example in mathematical finance. Such point sets are constructed either as digital nets (see the MinT database below) or as lattice rules (see the Encyclopaedia of Cubature Formulas below). Further information may be obtained from the links below and from several researchers in the field.

• The MC&QMC Home Page is a very useful starting point to this topic.
• MinT, the database for optimal (t, m, s)-net parameters, is a must for all those who want to use such low-discrepancy point sets in higher dimension. The MinT project is due to Wolfgang Schmid, a collegue of mine at the Department of Mathematics at Salzburg University.
• The Encyclopaedia of Cubature Formulas, maintained by Ronald Cools at Leuven University, Belgium, is also a most helpful address for information on low-discrepancy point sets and how to employ them to solve high-dimensional problems.
• Quasi-Monte Carlo links by Wolfgang Ch. Schmid, University Salzburg;
• IBM Research Publications offers several papers on quasi-Monte Carlo methods, mainly by a group around Shu Tezuka at the IBM Tokyo Research Laboratory, IBM Japan Ltd. (There is a search engine being provided by IBM.)
• Applications to computer graphics of quasi-Monte Carlo methods are studied by Alexander Keller and his group at the University of Ulm, Germany.
• The Centre for Mathematical & Statistical Modelling of Complex Systems at the University of New South Wales, Sydney, Australia, is home to the research group of Ian Sloan, one of the leading researchers on lattice methods in the QMC field.
• MathConsult Quasi-Random Streams
• Leading researchers like Niederreiter, Skriganov, Bierbrauer, Edel and others have pointed out the close relationship between digital (t,m,s)-nets and linear codes. Ives Edel offers an interesting database of codes for download.

back to the top

Research supported by