Skip to main content
SpringerLink
Log in

Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree

  • Published:
Computing Aims and scope Submit manuscript

Abstract.

We study cubature formulas for d-dimensional integrals with a high trigonometric degree. To obtain a trigonometric degree \(\ell\) in dimension d, we need about \(d^\ell/\ell !\) 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 different methods to obtain formulas with high trigonometric degree.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Department of Computer Science Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium, e-mail: ronald.cools@cs.kuleuven.ac.be , , , , , , BE

    R. Cools

  2. Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstraße 1 1/2, D-91054 Erlangen, Germany, e-mail: novak@mi.uni-erlangen.de , , , , , , DE

    E. Novak

  3. Fakultät für Mathematik und Informatik, Universität Passau, D-94030 Passau, Germany, e-mail: klaus.ritter@fmi.uni-passau.de , , , , , , DE

    K. Ritter

Authors
  1. R. Cools
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Novak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Ritter
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: April 8, 1998

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cools, R., Novak, E. & Ritter, K. Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree. Computing 62, 147–162 (1999). https://doi.org/10.1007/s006070050018

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s006070050018

Search

Navigation