演講公告
新聞標題： ( 2016-11-25 )
演講主題：High-dimensional integration of functions with kinks and jumps
主講人：Ian H. Sloan 教授 (University of New South Wales, Australia)
演講日期：2016年12月13日(星期二) 14:00 – 15:00
演講地點：(光復校區) 科學一館223室
茶會時間：當天下午1:30 (科學一館205室)
摘要內容：
In many applications, including option pricing, integrals of d-variate functions with “kinks”or “jumps” are encountered. (Kinks describe simple discontinuities in the derivative, jumps describe simple discontinuities in function values.) The standard analyses of sparse grid or Quasi Monte Carlo methods fail completely in the presence of kinks or jumps, yet the observed performance of these methods can remain reasonable. In recent joint papers with Michael Griebel and Frances Kuo we sought an explanation by showing that many terms of the ANOVA expansion of a function with kinks can be smooth, because of the smoothing effect of integration. The problem settings have included both the unit cube and d-dimensional Euclidean space. The underlying idea is that integration of a non-smooth function with respect to a well chosen variable, say xj , can result in a smooth function of d 􀀀 1 variables. In still more recent joint work with Andreas Griewank, Hernan Leovey and Frances Kuo we have extended the theoretical results from kinks to jumps, and have turned “preintegration” into a practical method for evaluating integrals of some non-smooth functions over d-dimensional Euclidean space. In this talk I will explain the concept of the ANOVA decomposition, the reason for smoothness in the ANOVA decomposition, and the method of“smoothing by preintegration”.
相關檔案：Talk _1051213.pdf
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