Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree

نویسندگان

  • Ronald Cools
  • Erich Novak
چکیده

We study cubature formulas for d-dimensional integrals with a high trigonometric degree. To obtain a trigonometric degreè in dimension d, we need about d ` =`! function values if d is large. Only a small number of arithmetical operations is needed to construct the cubature formulas using Smolyak's technique. We also compare diierent methods to obtain formulas with high trigonometric degree. Abstract. We study cubature formulas for d-dimensional integrals with a high trigonometric degree. To obtain a trigonometric degreè in dimension d, we need about d ` =`! function values if d is large. Only a small number of arithmetical operations is needed to construct the cubature formulas using Smolyak's technique. We also compare diierent methods to obtain formulas with high trigonometric degree.

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تاریخ انتشار 2010