Fast computation of Goursat’s infinite integral with very high accuracy

• 大浦, 拓哉

抄録

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.

収録刊行物

• Journal of Computational and Applied Mathematics

  Journal of Computational and Applied Mathematics 249 1-8, 2013-09

  Elsevier B.V.

キーワード

• Numerical quadrature
• Multiple-precision computation
• Double exponential quadrature method
• Computational complexity

詳細情報

• CRID: 1050845760697432576
• NII論文ID: 120005244245
• NII書誌ID: AA00696002
• ISSN: 03770427
• HANDLE: 2433/173114
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
  • IRDB
  • CiNii Articles