کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4642696 | 1341353 | 2007 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Type II Hermite-Padé approximation to the exponential function
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Type II Hermite-Padé approximation to the exponential function Type II Hermite-Padé approximation to the exponential function](/preview/png/4642696.png)
چکیده انگلیسی
We obtain strong and uniform asymptotics in every domain of the complex plane for the scaled polynomials a(3nz), b(3nz), and c(3nz) where a, b, and c are the type II Hermite-Padé approximants to the exponential function of respective degrees 2n+2, 2n and 2n, defined by a(z)e-z-b(z)=O(z3n+2) and a(z)ez-c(z)=O(z3n+2) as zâ0. Our analysis relies on a characterization of these polynomials in terms of a 3Ã3 matrix Riemann-Hilbert problem which, as a consequence of the famous Mahler relations, corresponds by a simple transformation to a similar Riemann-Hilbert problem for type I Hermite-Padé approximants. Due to this relation, the study that was performed in previous work, based on the Deift-Zhou steepest descent method for Riemann-Hilbert problems, can be reused to establish our present results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 207, Issue 2, 15 October 2007, Pages 227-244
Journal: Journal of Computational and Applied Mathematics - Volume 207, Issue 2, 15 October 2007, Pages 227-244
نویسندگان
A.B.J. Kuijlaars, H. Stahl, W. Van Assche, F. Wielonsky,