Skip to main content

Spline Blended Approximation of Multivariate Functions

  • Chapter
Polynomial and Spline Approximation

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 49))

  • 91 Accesses

Abstract

Spline and polynomial blended approximants to a multivariate function are synthesized from approximations to univariate samplings of the function. General algebraic and analytic properties of blended and tensor product interpolants are reviewed.

Partially supported by USAF Office of Scientific Research Contract No. F44620-76-C-0104.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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. G. Birkhoff and C. DeBoor, “Piecewise Polynomial Interpolation and Approximation,” in Approximation Functions, H. Garabedian, ed., 164–190 Amsterdam, Elsevier, 1965.

    Google Scholar 

  2. R. E. Carlson and C. A. Hall, “Error Bounds for Bicubic Spline Interpolation,” J. Approx. Theory, 7, 41–47, (1973).

    Article  MATH  MathSciNet  Google Scholar 

  3. J. C. Cavendish, W. J. Gordon, and C. A. Hall, “Ritz-Galerkin Approximations in Blending Function Spaces,” Numer, Math., 26, 155–178 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  4. C. DeBoor, “Bicubic Spline Interpolation,” J. Math, and Phys., 41, 212–218, (1962).

    MathSciNet  Google Scholar 

  5. W. J. Gordon, “Spline-Blended Surface Interpolation Through Curve Networks,” J. Math. Mech., 10, 931–952, (1968).

    Google Scholar 

  6. W. J. Gordon, “Distributive Lattices and the Approximation of Multivariate Functions,” in Approximation with Special Emphasis on Spline Functions, 223–277, I. J. Schoenberg, ed., New York, Academic Press, 1969.

    Google Scholar 

  7. W. J. Gordon and C. A. Hall, “Transfinite Element Methods: Blending-Function Interpolation Over Curved Element Domains,” Numer. Math. 21, 109–129, (1973).

    Article  MATH  MathSciNet  Google Scholar 

  8. C. A. Hall, “Transfinite Interpolation and Applications to Engineering Applications,” in Theory of Approximation with Applications, eds., A. Law and B. Sahney, Academic Press, 1976.

    Google Scholar 

  9. M. Schultz and R. S. Varga, “L-splines,” Numer. Math., 10, 345–369, (1967).

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Schultz, “L°°-multivariate Approximation Theory,” SIAM J. Numer. Analysis, 6, 161–183, (1969).

    MATH  Google Scholar 

  11. M. Schultz, “L∞-multivariate Approximation Theory,” SIAM J. Numer. Analysis, 6, 184–209, (1969).

    MATH  Google Scholar 

  12. M. Schultz, Spline Analysis, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1973.

    MATH  Google Scholar 

  13. B. K. Swartz and R. S. Varga, “Error Bounds for Spline and L-spline Interpolation,” J. Approx. Theory 6, 6–149, (1972).

    Article  MATH  MathSciNet  Google Scholar 

  14. R. S. Varga, Functional Analysis and Approximation Theory in Numerical Analysis, SIAM, 1972.

    Google Scholar 

  15. D. S. Watkins, “Error Bounds for Polynomial Blending Function Methods,” SIAM J. Numer. Analysis, 14, 721–734.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Hall, C. (1979). Spline Blended Approximation of Multivariate Functions. In: Sahney, B.N. (eds) Polynomial and Spline Approximation. NATO Advanced Study Institutes Series, vol 49. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9443-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-9443-0_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-9445-4

  • Online ISBN: 978-94-009-9443-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics