کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5773839 | 1631462 | 2017 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
(s,lnκ)-weak tractability of linear problems
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We introduce a new notion of tractability for multivariate problems, namely (s,lnκ)-weak tractability for positive s and κ. This allows us to study the information complexity of a d-variate problem with respect to different powers of d and the bits of accuracy lnεâ1. We consider the worst case error for the absolute and normalized error criteria. We provide necessary and sufficient conditions for (s,lnκ)-weak tractability for general linear problems and linear tensor product problems defined over Hilbert spaces. In particular, we show that non-trivial linear tensor product problems cannot be (s,lnκ)-weakly tractable when sâ(0,1] and κâ(0,1]. On the other hand, they are (s,lnκ)-weakly tractable for κ>1 and s>1 if the univariate eigenvalues of the linear tensor product problem enjoy a polynomial decay. Finally, we study (s,lnκ)-weak tractability for the remaining combinations of the values of s and κ.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 40, June 2017, Pages 1-16
Journal: Journal of Complexity - Volume 40, June 2017, Pages 1-16
نویسندگان
A. Papageorgiou, I. Petras, H. Woźniakowski,