An improved convergence test for the double exponential formula

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  • OOURA Takuya
    Research Institute for Mathematical Sciences, Kyoto University

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  • 二重指数関数型数値積分公式の収束判定法の改良
  • ニジュウ シスウ カンスウガタ スウチ セキブン コウシキ ノ シュウソク ハンテイホウ ノ カイリョウ

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The double exponential formula is well-known as a powerful numerical quadrature rule. The automatic quadrature routine of the double exponential formula is necessary for the procedure of checking the convergence, but the conventional method of estimating discretization error is too simple to have a reliable estimate. In this paper, we propose a new method which robustly estimates the discretization error quite effectively.

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