Methods for generating random orthogonal matrices. (English) Zbl 0941.65027
Niederreiter, Harald (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 1998. Proceedings of a conference held at the Claremont Graduate Univ., Claremont, CA, USA, June 22-26, 1998. Berlin: Springer. 199-213 (2000).
Summary: Random orthogonal matrices are used to randomize integration methods for \(n\)-dimensional integrals over spherically symmetric integration regions. Currently available methods for the generation of random orthogonal matrices are reviewed, and some methods for the generation of quasi-random orthogonal matrices are proposed. These methods all have \(O(n^3)\) time complexity. Some new methods to generate both random and quasi-random orthogonal matrices will be described and analyzed. The new methods use products of butterfly matrices, and have time complexity \(O(\log(n)n^2)\). The use of these methods will be illustrated with results from the numerical computation of high-dimensional integrals from a computational finance application.
For the entire collection see [Zbl 0924.00041].
For the entire collection see [Zbl 0924.00041].
MSC:
| 65D32 | Numerical quadrature and cubature formulas |
| 60H25 | Random operators and equations (aspects of stochastic analysis) |
| 65C50 | Other computational problems in probability (MSC2010) |
| 65C05 | Monte Carlo methods |
| 65F30 | Other matrix algorithms (MSC2010) |
