Skip to main content

New Applications of Taylor Model Methods

  • Chapter
  • First Online:
Automatic Differentiation of Algorithms

Abstract

Taylor model methods unify many concepts of high-order computational differentiation with verification approaches covering the Taylor remainder term. Not only do they provide local multivariate derivatives, they also allow for highly efficient and sharp verification. We present several recent results obtained with Taylor model methods, including verified optimization, verified quadrature and verified propagation of extended domains of initial conditions through ODEs, approaches towards verified solution of DAEs and PDEs. In all cases, the methods allow the development of new numeric-analytic tools that efficiently capitalize on the availability of derivatives and sharp inclusions over extended ranges. Applications of the methods are given, including global optimization, very high-dimensional numeric quadrature, particle accelerators, and dynamics of near-earth asteroids.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media New York

About this chapter

Cite this chapter

Makino, K., Berz, M. (2002). New Applications of Taylor Model Methods. In: Corliss, G., Faure, C., Griewank, A., Hascoët, L., Naumann, U. (eds) Automatic Differentiation of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0075-5_43

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0075-5_43

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6543-6

  • Online ISBN: 978-1-4613-0075-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics