کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4639061 | 1632031 | 2014 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Superfast solution of linear convolutional Volterra equations using QTT approximation
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
We address a linear fractional differential equation and develop effective solution methods using algorithms for the inversion of triangular Toeplitz matrices and the recently proposed QTT format. The inverses of such matrices can be computed by the divide and conquer and modified Bini’s algorithms, for which we present the versions with the QTT approximation. We also present an efficient formula for the shift of vectors given in QTT format, which is used in the divide and conquer algorithm. As a result, we reduce the complexity of inversion from the fast Fourier level O(nlogn)O(nlogn) to the speed of superfast Fourier transform, i.e., O(log2n)O(log2n). The results of the paper are illustrated by numerical examples.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 260, April 2014, Pages 434–448
Journal: Journal of Computational and Applied Mathematics - Volume 260, April 2014, Pages 434–448
نویسندگان
Jason A. Roberts, Dmitry V. Savostyanov, Eugene E. Tyrtyshnikov,