Skip to main content

Nonlinear approximation problems in vector norms

Part of the Lecture Notes in Mathematics book series (LNM,volume 630)

Keywords

  • Stationary Point
  • Full Rank
  • Descent Step
  • Smooth Norm
  • Haar Condition

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
Price excludes VAT (Canada)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anderson, D H and M R Osborne (1976). Discrete, linear approximation problems in polyhedral norms, Num. Math. 26, 179–189.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Anderson, D H and M R Osborne (1977a). Discrete, non-linear approximation problems in polyhedral norms, Num. Math. 28, 143–156.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Anderson, D H and M R Osborne (1977b). Discrete, non-linear approximation problems in polyhedral norms: a Levenberg-like algorithm. Num. Math. 28, 157–170.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Barrodale, I and F D K Roberts (1973). An improved algorithm for discrete ℓ1 linear approximation, SIAMJ Num. Anal. 10, 839–848.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Bartels, R H, A R Conn and J W Sinclair (1977). Minimisation techniques for piecewise differentiable functions — the ℓ1 solution to an over-determined linear system, SIAMJ Num. Anal. (to appear).

    Google Scholar 

  • Cheney, E W (1966). Introduction to Approximation Theory, McGraw-Hill, New York.

    MATH  Google Scholar 

  • Cline, A K (1976). A descent method for the uniform solution to overdetermined systems of linear equations, SIAMJ Num. Anal. 13, 293–309.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Fletcher, R, J A Grant and M D Hebden (1971). The calculation of linear best Lp approximations, Computer J. 14, 276–279.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Kelley, J E (Jr) (1958). An application of linear programming to curve fitting, SIAMJ 6, 15–22.

    MathSciNet  MATH  Google Scholar 

  • Madsen, K (1975). An algorithm for minimax solutions of overdetermined systems of non-linear equations, JIMA 16, 321–328.

    MathSciNet  MATH  Google Scholar 

  • Osborne, M R (1972). An algorithm for discrete, non-linear best approximation Problems: In: Numerische Methoden der Approximationstheorie, Band 1, eds. L Collatz and G Meinardus. Birkhauser-Verlag.

    Google Scholar 

  • Osborne, M R (1977). Nonlinear least squares — the Levenberg algorithm revisited, J. Aust. Math. Soc., Series B (to appear).

    Google Scholar 

  • Osborne, M R and G A Watson (1969). An algorithm for minimax approximation in the non-linear case, Computer J. 12, 64–69.

    MathSciNet  MATH  Google Scholar 

  • Osborne, M R and G A Watson (1971). On an algorithm for non-linear L1 approximation, Computer J. 14, 184–188.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Rockafellar, R T (1970). Convex Analysis, Princeton, New Jersey. Princeton Univ. Press.

    CrossRef  MATH  Google Scholar 

  • Stiefel, E L (1959). Über diskrete und lineare Tschebyscheff-Approximationen, Num. Math. 1, 1–28.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Watson, G A (1974). The calculation of best restricted approximations, SIAMJ Num. Anal. 11, 693–699.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1978 Springer-Verlag

About this paper

Cite this paper

Osborne, M.R., Watson, G.A. (1978). Nonlinear approximation problems in vector norms. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067701

Download citation

  • DOI: https://doi.org/10.1007/BFb0067701

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08538-6

  • Online ISBN: 978-3-540-35972-2

  • eBook Packages: Springer Book Archive