Research on visualization of the double exponential transformation

双指数变换的可视化研究

• 批准号: 09650077
• 负责人: MORI Masatake
• 金额: $ 1.92万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09650077/
• 关键词: numerical integration; double exponential transformation; double exponential formula; complex function theory; characteristic function of the error; visualization; computer graphics; Sinc近似

The head investigator arid others have proposed a family of efficent formulas for numerical integration called the double exponential formula. On the other hand, the error of numerical integration can be expressed in terms of a complex integral of a product of the integrand and a function called the characteristic function of the error. In this research we developed a system which computes the characteristic function of the error and gives its contour map on a graphic display. If we.. use this system we can estimate the error of numerical integration by the double exponential formula easily and accurately.The head investigator and opthers had already written several programs which individually compute the characteristic function of the error of sonic particular integral and give its contour map. In the present research we treated the characteristic function in a unified way and developed a system which gives the contour map automatically if the user specifies the parameters such as the type of the integral, the interval of integration, etc. Also in this system we included the*Ooura's formula which compute efficiently Fourier type integrals. Furthermore, we developed a system which ti-eats Newton-Cotes formulas and Gauss type formulas. These programs are written in DIGITAL Visual Fortran, and run on a Windows 95 personal computer system.Finally we developed a system to specify the parameters through several input windows which runs on Microsoft Visual Basic. We wrote a manual to use this system and included it in the report of the present research together with the entire source. code.

首席研究员和其他人提出了一系列有效的数值积分公式，称为双指数公式。另一方面，数值积分的误差可以用被积函数和称为误差特征函数的函数的乘积的复积分来表示。在这项研究中，我们开发了一个系统，计算的特征函数的误差，并给出其等值线图的图形显示。如果我们利用该系统，可以方便、准确地用双指数公式估计数值积分的误差，课题组组长和同行已编写了几个程序，分别计算了声波特殊积分误差的特征函数，并给出了其等值线图。在本研究中，我们处理的特征函数在一个统一的方式，并开发了一个系统，如果用户指定的参数，如积分的类型，积分的区间等，它会自动给出等值线图也在这个系统中，我们包括 *Ooura的公式，有效地计算傅立叶型积分。在此基础上，我们还发展了一个系统，该系统可以同时使用Newton-Cotes公式和Gauss型公式。这些程序都是用DIGITAL Visual Fortran语言编写的，在Windows 95个人计算机上运行，最后在Microsoft Visual Basic上开发了一个通过多个输入窗口指定参数的系统。我们写了一本使用该系统的手册，并将其与整个源代码一起包含在本研究的报告中。代码.

项目成果

Mori, Masatake: "The double exponential transformation in numerical analysis (in Japanese)" Bulletin of Japan SIAM. 8. 77-80 (1998)

Mori, Masatake：“数值分析中的双指数变换（日语）”日本 SIAM 公报。

森正武: "二重指数関数型変換(DE変換)のすすめ" 応用数理. 8巻4号. 77-80 (1998)

Masatake Mori：“双指数变换（DE 变换）的推荐”应用数学，第 8 卷，第 4 期，77-80（1998 年）。

杉原正顕: "二重指数関数型変換を用いたSine関数近似" 京都大学数理解析研究所講究録. 990号. 125-135 (1997)

Masaaki Sugihara：“使用双指数变换的正弦函数近似”京都大学数学科学研究所 Kokyuroku No. 990. 125-135 (1997)。

森正武: "二重指数関数型変換(DE変換)のすすめ" 応用数理. 8巻. 77-80 (1998)

Masatake Mori：“双指数变换（DE 变换）的推荐”应用数学卷 8. 77-80（1998）。

Sugihara, Masaaki: "Sinc approximation based on the double exponentisl transformation (in Japanese)" Kokyuroku, RIMS Kyoto University. No.999. 125-135 (1997)

Sugihara, Masaaki：“基于双指数变换的 Sinc 近似（日语）”Kokyuroku，RIMS 京都大学。