Methods for Generating Random Orthogonal Matrices
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.
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