By Arieh Iserles

ISBN-10: 0521643163

ISBN-13: 9780521643160

Acta Numerica is an annual quantity featuring great survey articles in numerical research and clinical computing. the themes and authors are selected by way of a exclusive overseas Editorial Board in order to document crucial and well timed advancements within the topic in a way obtainable to the broader neighborhood of execs with an curiosity in clinical computing.

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Additional resources for Acta Numerica 1998 (Volume 7)

Sample text

Similar results have been obtained on problems from computational finance by Caflisch, Morokoff and Owen (19976). 7. Monte Carlo methods for rarefied gas dynamics Computations for rarefied gas dynamics, as occur in the outer parts of the atmosphere, are difficult since the gas is represented by a distribution func­ tion over space, time and molecular velocity.  One reason for including this application of Monte Carlo in this survey is that formulation of an effective Monte Carlo method in the fluid dynamic limit is an open problem.

Our experience is that V[f] in Koksma­Hlawka is usually a gross over­ estimate, while the discrepancy is indicative of actual performance. MONTE CARLO AND QUASI­MONTE CARLO 27 A further, more subtle point is that for standard Monte Carlo each point is an estimate of the entire integral. A typical quasi­random sequence, on the other hand, has a hierarchical structure, so that the initial points sample the integrand on a coarse scale and later points sample it on a finer scale. This is the source of the log N terms in the discrepancy bounds cited below.

J. Hickernell (1998), 'A generalized discrepancy and quadrature error bound', Math. Comput. 67, 299­322. R.  T. Craig (1995), Introduction to Mathematical Statistics, Pren­ tice Hall. L. K. Hua and Y. Wang (1981), Applications of Number Theory to Numerical Analysis, Springer, Berlin/New York. S. Jin and C. D. Levermore (1993), 'Fully­discrete numerical transfer in diffusive regimes', Transp. Theory Statist. Phys. 22, 739­791.  Toscani (1998), 'Diffusive relaxation schemes for discrete­ velocity kinetic equations'.

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Acta Numerica 1998 (Volume 7) by Arieh Iserles

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