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<p>Techniques of variable transformation such as the double exponential (DE) transformation and the IMT have become well known in numerical integration. Recently, the DE transformation has also been applied to various computation tasks, such as numerical indefinite integration and solving integral equations and ordinary differential equations using the Sinc approximation. Herein, the author demonstrates that the IMT-double exponential (IMT-DE) transformation used in the IMT-DE numerical integration formula, which is a modified form of the IMT formula, can be applied for function approximation when using the Sinc approximation method for periodic functions. It is expected that the IMT-DE transformation can be applied to various computation tasks other than numerical integration via the presented function approximation method. There is also a relationship between the presented method and the method based on the DE transformation and the Sinc approximation in the sense that the latter is obtained by taking a limit in the former. </p>

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Function approximation method based on the IMT-double exponential transformation and the Sinc approximation for periodic functions

  • 期刊论文

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  • 发表日期：

    2025年9月8日

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  • Hidenori Ogata

摘要

Techniques of variable transformation such as the double exponential (DE) transformation and the IMT have become well known in numerical integration. Recently, the DE transformation has also been applied to various computation tasks, such as numerical indefinite integration and solving integral equations and ordinary differential equations using the Sinc approximation. Herein, the author demonstrates that the IMT-double exponential (IMT-DE) transformation used in the IMT-DE numerical integration formula, which is a modified form of the IMT formula, can be applied for function approximation when using the Sinc approximation method for periodic functions. It is expected that the IMT-DE transformation can be applied to various computation tasks other than numerical integration via the presented function approximation method. There is also a relationship between the presented method and the method based on the DE transformation and the Sinc approximation in the sense that the latter is obtained by taking a limit in the former.