کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8901647 | 1631945 | 2019 | 28 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm
ترجمه فارسی عنوان
برآورد خطای عقب مانده برای تقریب ماتریس نمایشی توسط الگوریتم تیلور
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
In this paper we show that it is possible to estimate the backward error for the approximation of the matrix exponential on-the-fly, without the need to precompute in high precision quantities related to specific accuracies. In this way, the scaling parameter s
and the degree m of the truncated Taylor series (the underlying method) are adapted to the input matrix and not to a class of matrices sharing some spectral properties, such as with the classical backward error analysis. The result is a very flexible method which can approximate the matrix exponential at any desired accuracy. Moreover, the risk of overscaling, that is the possibility to select a value s larger than necessary, is mitigated by a new choice as the sum of two powers of two. Finally, several numerical experiments in MATLAB with data in double and variable precision and with different tolerances confirm that the method is accurate and often faster than available good alternatives.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 346, 15 January 2019, Pages 532-548
Journal: Journal of Computational and Applied Mathematics - Volume 346, 15 January 2019, Pages 532-548
نویسندگان
M. Caliari, F. Zivcovich,