Type of Document Dissertation Author Chi, Hongmei Author's Email Address email@example.com URN etd-07062004-140409 Title Scrambled Quasirandom Sequences and Their Applications Degree Doctor of Philosophy Department Computer Science, Department of Advisory Committee
Advisor Name Title Michael Mascagni Committee Chair Ashok Srinivasan Committee Member Mike Burmester Committee Member Robert van Engelen Committee Member Sam Huckaba Committee Member Keywords
- Parallel Computing
- Randomized Quasi-Monte Carlo Methods
- Optimal Sequences
- Automatic Error Estimation
Date of Defense 2004-06-04 Availability unrestricted AbstractQuasi-Monte Carlo methods are a variant of
ordinary Monte Carlo methods that employ highly
uniform quasirandom numbers in place of Monte Carlo's pseudorandom numbers. Monte Carlo methods offer statistical error estimates; however, while quasi-Monte Carlo has a faster convergence rate than normal Monte Carlo, one cannot obtain error
estimates from quasi-Monte Carlo sample values by any practical way. A recently proposed method, called randomized quasi-Monte Carlo methods,
takes advantage of Monte Carlo and
quasi-Monte Carlo methods. Randomness can
be brought to bear on quasirandom sequences through scrambling and
other related randomization techniques in randomized quasi-Monte Carlo methods, which
provide an elegant approach to obtain error estimates for quasi-Monte Carlo based on treating each scrambled sequence as a different and independent random sample. The core of randomized quasi-Monte Carlo is to find an effective and
fast algorithm to scramble (randomize) quasirandom sequences. This dissertation surveys research on algorithms and implementations of scrambled quasirandom sequences and proposes some new algorithms to improve the quality of scrambled quasirandom sequences.
Besides obtaining error estimates for quasi-Monte Carlo, scrambling techniques provide a natural way to parallelize quasirandom sequences.
This scheme is especially suitable for distributed or grid computing.
By scrambling a quasirandom sequence we can produce a family of related
quasirandom sequences. Finding one or a subset of optimal quasirandom sequences within this family is an interesting problem, as such optimal quasirandom sequences can be quite useful
for quasi-Monte Carlo. The process of finding such optimal quasirandom sequences is called the derandomization of a randomized (scrambled) family. We summarize aspects of this
technique and propose some new algorithms for finding optimal sequences from the Halton, Faure and Sobol sequences. Finally we
explore applications of derandomization.
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