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Title: | Fast computation of Goursat’s infinite integral with very high accuracy |
Authors: | Ooura, Takuya ![]() ![]() |
Author's alias: | 大浦, 拓哉 |
Keywords: | Numerical quadrature Multiple-precision computation Double exponential quadrature method Computational complexity |
Issue Date: | Sep-2013 |
Publisher: | Elsevier B.V. |
Journal title: | Journal of Computational and Applied Mathematics |
Volume: | 249 |
Start page: | 1 |
End page: | 8 |
Abstract: | We propose an efficient computation method for the infinite integral View the MathML source, whose integrand contains a series of spikes, approximately π apart, growing taller and narrower as x increases. Computing the value of this integral has been a problem since 1984. We herein demonstrate a method using the Hilbert transform for changing this type of singular function into a smooth function and computing the value of the integral to more than one million significant digits using a superconvergent double exponential quadrature method. |
Rights: | © 2013 Elsevier B.V. This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。 |
URI: | http://hdl.handle.net/2433/173114 |
DOI(Published Version): | 10.1016/j.cam.2013.02.006 |
Appears in Collections: | Journal Articles |

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