Skip to main content
SpringerLink
Log in

Numerical Steepest Descent

  • Reference work entry
  • First Online:
Book cover Encyclopedia of Applied and Computational Mathematics

  • 124 Accesses

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 999.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 999.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 999.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Asheim, A., Huybrechs, D.: Asymptotic analysis of numerical steepest descent with path approximations. Found. Comput. Math. 10(6), 647–671 (2010). doi:10.1007/s10208-010-9068-y

    Article  MathSciNet  MATH  Google Scholar 

  2. Davis, P.J., Rabinowitz, P.: Methods of Numerical Integration. Computer Science and Applied Mathematics. Academic, New York (1984)

    MATH  Google Scholar 

  3. Deaño, A., Huybrechs, D.: Complex Gaussian quadrature of oscillatory integrals. Numer. Math. 112(2), 197–219 (2009). doi:10.1007/s00211-008-0209-z

    Article  MathSciNet  MATH  Google Scholar 

  4. Debye, P.: Näherungsformeln für die Zylinderfunktionen für grosse Werte des Arguments und unbeschränkt veranderliche Werte des Index. Math. Ann. 67(4), 535–558 (1909). doi:10.1007/BF01450097

    Article  MathSciNet  MATH  Google Scholar 

  5. Franklin, J., Friedman, B.: A convergent asymptotic representation for integrals. Proc. Camb. Philos. Soc. 53, 612–619 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gautschi, W.: Orthogonal Polynomials: Computation and Approximation. Clarendon Press, Oxford (2004)

    MATH  Google Scholar 

  7. Huybrechs, D., Olver, S.: Superinterpolation in highly oscillatory quadrature. Found. Comput. Math. (2011). doi:10.1007/s10208-011-9102-8

    MathSciNet  MATH  Google Scholar 

  8. Huybrechs, D., Vandewalle, S.: On the evaluation of highly oscillatory integrals by analytic continuation. SIAM J. Numer. Anal. 44(3), 1026–1048 (2006). doi:10.1137/050636814

    Article  MathSciNet  MATH  Google Scholar 

  9. Huybrechs, D., Vandewalle, S.: The construction of cubature rules for multivariate highly oscillatory integrals. Math. Comput. 76(260), 1955–1980 (2007). doi:10.1090/S0025-5718-07-01937-0

    Article  MathSciNet  MATH  Google Scholar 

  10. Wong, R.: Asymptotic Approximation of Integrals. SIAM, Philadelphia (2001)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, K.U. Leuven, Leuven, Belgium

    Daan Huybrechs

Authors
  1. Daan Huybrechs
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Texas at Austin, Austin, TX, USA

    Björn Engquist

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this entry

Cite this entry

Huybrechs, D. (2015). Numerical Steepest Descent. In: Engquist, B. (eds) Encyclopedia of Applied and Computational Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70529-1_318

Download citation

Publish with us

Policies and ethics

Search

Navigation