Acta Numerica 1998 (Volume 7) by Arieh Iserles

By Arieh Iserles

Acta Numerica is an annual quantity proposing significant survey articles in numerical research and clinical computing. the topics and authors are selected through a exceptional overseas Editorial Board for you to document an important and well timed advancements within the topic in a fashion available to the broader neighborhood of execs with an curiosity in medical computing.

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Zinterhof, eds), Springer.  Neunzert, J.  Wiesen (1990), 'Application of well­distributed sequences to the numerical simulation of the Boltzmann equation', J. Comput. Appl.  31, 15­22.  Bardos, F.  Formal derivations', J. Statist.  63, 323­344.  Bardos, F.  Convergence proofs for the Boltzmann equation', Comm. Pure Appl.  46, 667­753.  Bird (1976), Molecular Gas Dynamics, Oxford University Press. G. A. Bird (1978), 'Monte Carlo simulation of gas flows', Ann. Rev. Fluid Mech. 10, 11­31.  Adams (1992), 'The asymptotic diffusion limit of a linear discontinuous discretization of a two­dimensional linear transport equation', J.

Since there is no Central Limit Theorem for quasi­random sequences, there is no corresponding empirical error estimate for quasi­Monte Carlo. On the other hand, confidence in the accuracy of quasi­Monte Carlo integration comes from refining a set of computations. MONTE CARLO AND QUASI­MONTE CARLO 31 Second, quasi­Monte Carlo methods are designed for integration and are not directly applicable to simulation. This is because of the correlations between the points of a quasi­random sequence. However, in many simula­ tions the desired result is an expectation of some quantity, which can then be written as a high­dimensional integral on which quasi­Monte Carlo can be used.

Formal derivations', J. Statist.  63, 323­344.  Bardos, F.  Convergence proofs for the Boltzmann equation', Comm. Pure Appl.  46, 667­753.  Bird (1976), Molecular Gas Dynamics, Oxford University Press. G. A. Bird (1978), 'Monte Carlo simulation of gas flows', Ann. Rev. Fluid Mech. 10, 11­31.  Adams (1992), 'The asymptotic diffusion limit of a linear discontinuous discretization of a two­dimensional linear transport equation', J. Comput.  98, 285­300. P.  L. Fox and H. Niederreiter (1994), 'Algorithm 738 ­ Programs to generate Niederreiter's discrepancy sequences', A CM Trans.

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