کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4608813 | 1631473 | 2011 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Complexity of numerical integration over spherical caps in a Sobolev space setting
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
If positive weight rules Qm(n) with m(n) nodes in C(z;γ) and polynomial degree of exactness n have m(n)â¼nr nodes, then the worst-case error is bounded above by cËr,s,γ(m(n))âs/r, giving the same order mâs/r as in the lower bound. Thus the complexity in Hs(Sr) of numerical integration over C(z;γ) with m nodes is of the order mâs/r. The constants cr,s,γ and cËr,s,γ in the lower and upper bounds do not depend in the same way on the area |C(z;γ)|â¼Î³r of the cap. A possible explanation for this discrepancy in the behavior of the constants is given. We also explain how the lower and upper bounds on the worst-case error in a Sobolev space setting can be extended to numerical integration over a general non-empty closed and connected measurable subset Ω of Sr that is the closure of an open set.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 27, Issues 3â4, JuneâAugust 2011, Pages 383-403
Journal: Journal of Complexity - Volume 27, Issues 3â4, JuneâAugust 2011, Pages 383-403
نویسندگان
Kerstin Hesse,