کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9501286 | 1338399 | 2005 | 47 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces](/preview/png/9501286.png)
چکیده انگلیسی
We also investigate the worst-case error of integration in weighted Sobolev spaces. As the main tool we define a digital shift invariant kernel associated to the kernel of the weighted Sobolev space. This allows us to study the mean square worst-case error of randomly digitally shifted digital (t,m,s)-nets. As this digital shift invariant kernel is almost the same as the kernel for the Hilbert space based on Walsh functions, we can derive results for the weighted Sobolev space based on the analysis of the Walsh function space. We show that there exists a (t,m,s)-net which achieves the best possible convergence order for integration in weighted Sobolev spaces and are strongly tractable under the same condition on the weights as for lattice rules.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 21, Issue 2, April 2005, Pages 149-195
Journal: Journal of Complexity - Volume 21, Issue 2, April 2005, Pages 149-195
نویسندگان
Josef Dick, Friedrich Pillichshammer,