Skip to main content

Three Scale Versus Matrix Refinement Equations

  • Conference paper
  • 107 Accesses

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

Abstract

We show under what conditions three scale refinement equations are equivalent to matrix refinement equations of a certain structure, and how this equivalence can be used in the modification of refinement masks.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Conti, K. Jetter: A new subdivision method for bivariate splines on the four-directional mesh, J. Comput. Appl. Math. 119 (2000), 936–952.

    Article  MathSciNet  Google Scholar 

  2. C. Conti, G. Zimmermann: Interpolatory vector subdivision schemes, submitted.

    Google Scholar 

  3. S. Dekel, N. Dyn: Poly-scale refinability and subdivision, Appl. Comput. Harmon. Anal. 13 (2002), 35–62.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Dubuc: Interpolation through an iterative scheme, J. Math. Anal. Appl. 114 (1986), 185–204.

    Article  MATH  MathSciNet  Google Scholar 

  5. N. Dyn, J. A. Gregory, D. Levin: A four-point interpolatory subdivision scheme for curve design, Comput. Aided Geom. Design 4 (1987), 257–268.

    MATH  MathSciNet  Google Scholar 

  6. T. Goodman: Pairs of refinable bivariate splines, In: Advanced Topics in Multivariate Approximation, Approximations and Decompositions Vol. 8, 125–138, World Scientific, Singapore 1996.

    Google Scholar 

  7. K. Jetter, G. Zimmermann: Polynomial reproduction in subdivision, Adv. Comp. Math., to appear (2002).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Basel AG

About this paper

Cite this paper

Zimmermann, G. (2003). Three Scale Versus Matrix Refinement Equations. 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_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8067-1_18

  • 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