Skip to main content
SpringerLink
Log in

How to Generate Smoother Refinable Functions from Given Ones

  • Conference paper
Book cover Modern Developments in Multivariate Approximation

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 145))

Abstract

We consider the question of how and to what extent the simple process of smoothing refinable functions by creating an additional zero at —1 of the associated symbol can be transferred to the multivariate case.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
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.

References

  1. A. S. Cavaretta, W. Dahmen, C. A. Micchelli: Stationary Subdivision, Memoirs Amer. Math. Soc. 93, Providence, R. I., 1991.

    Google Scholar 

  2. D. Cox, J. Little, D. O’Shea: Ideals, Varieties and Algorithms, Springer, New York—Berlin—Heidelberg—Tokyo, 1996.

    Google Scholar 

  3. W. Dahmen, C. A. Micchelli: Biorthogonal wavelet expansions, Constr. Approx. 13 (1997), 294–328.

    Google Scholar 

  4. N. Dyn: Subdivision schemes in Computer Aided Geometric Design, In: Advances in Numerical Analysis — Volume II, Wavelets,Subdivision Algorithms and Radial Basis Functions, W. Light (ed.), 36–104, Clarendon, Oxford, 1992.

    Google Scholar 

  5. K. Jetter, G. Plonka: A survey on L2-approximation order from shift-invariant spaces,In: Multivariate Approximation and Applications, N. Dyn, D. Leviatan, D. Levin, A. Pinkus (eds.), 73–111, Cambridge University Press, Cambridge, 2001.

    Chapter  Google Scholar 

  6. V. Latour, J. Müller, W. Nickel: Stationary subdivision for general scaling matrices, Math. Z. 227 (1998), 645–661.

    Article  MATH  MathSciNet  Google Scholar 

  7. C. A. Micchelli, T. Sauer: Regularity of multiwavelets, Advances Comput. Math. 7 (1997), 455–545.

    MATH  MathSciNet  Google Scholar 

  8. C. A. Micchelli, T. Sauer: On vector subdivision, Math. Z. 229 (1998), 621–674.

    Article  MATH  MathSciNet  Google Scholar 

  9. H. M. Möller, F. Mora: New constructive methods in classical ideal theory, J. Alg. 100 (1986), 138–178.

    Article  MATH  Google Scholar 

  10. H. M. Möller, T. Sauer: Multivariate refinable functions of high approximation order via quotient ideals of Laurent polynomials, Advances Comput. Math., to appear.

    Google Scholar 

  11. T. Sauer: Polynomial interpolation, ideals and approximation order of refinable functions, Proc. Amer. Math. Soc. 130 (2002), 3335–3347.

    Article  MATH  MathSciNet  Google Scholar 

  12. T. Sauer: Subdivisión vectorial estacionaria: ideales cociente,diferencias y potencia de aproximación, Rev. R. Acad. Cienc. Serie A. Mat. 96 (2002), 257–277.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Numerische Mathematik Justus-Liebig-Universität Gießen Heinrich-Buff-Ring 44, D-34592, Gießen, Germany

    Tomas Sauer

Authors
  1. Tomas Sauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mathematisches Institut, Gerhard-Mercator-Universität Duisburg, 47048, Duisburg, Germany

    Werner Haussmann

  2. Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, 70593, Stuttgart, Germany

    Kurt Jetter

  3. Fachbereich Mathematik, Universität Dortmund, 44221, Dortmund, Germany

    Manfred Reimer  & Joachim Stöckler  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Basel AG

About this paper

Cite this paper

Sauer, T. (2003). How to Generate Smoother Refinable Functions from Given Ones. In: Haussmann, W., Jetter, K., Reimer, M., Stöckler, J. (eds) Modern Developments in Multivariate Approximation. International Series of Numerical Mathematics, vol 145. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8067-1_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8067-1_16

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9427-2

  • Online ISBN: 978-3-0348-8067-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation