Skip to main content

Vector-Valued Polynomial and Spline Approximation

  • Chapter
Polynomial and Spline Approximation

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

  • 101 Accesses

Abstract

Blended interpolation of vector-valued functions is discussed relative to their applications in the construction of finite elements, mesh generation and table look-up of thermodynamic properties of a gas or liquid. The invertibi1ity of two isoparametric transformations is investigated.

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.

Similar content being viewed by others

References

  1. J. H. Ahlberg, E. N. Nilson and J. L. Walsh, The Theory of Splines and Their Applications, Academic Press, New York, 1967.

    MATH  Google Scholar 

  2. S. A. Coons, ‘Surfaces for computer-aided design of space forms’, Project MAC, Design Div., Dept. Mech. Engng., Mass. Inst. Tech. (1964). Available from: Clearinghouse for Federal Scientific-Technical Information, National Bureau of Standards, Springfield, Va., U.S.A.

    Google Scholar 

  3. P.G. Ciarlet and P. A. Raviart, “interpolation Theory Over Curved Elements with Applications to Finite Element Methods”, Compute. Methods Appl. Mech. Enng. 1, pp. 217–249 (1972).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. E. Frey, C. A. Hall and T. A. Porsching, “Some Results on the Global Inversion of Bilinear and Quadratic Isoparametric Finite Element Transformations”, Math, of Comp. 32 (to appear).

    Google Scholar 

  5. A. E. Frey, C. A. Hall and T. A. Porsching, “S0LV8: Inversion by Elimination of the 8-Node Quadratic Isoparametric Mapping”, (submitted).

    Google Scholar 

  6. W. J. Gordon, ‘Free-form surface interpolation through curve networks’, Res. Rept. 921, General Motors, Warren, Mich., U.S.A. (1969).

    Google Scholar 

  7. W. J. Gordon, ‘Spline-blended surface interpolation through curve networks’, J. Math. Mech., 18, 931–952 (1969).

    MATH  MathSciNet  Google Scholar 

  8. W. J. Gordon, ‘Blending-function methods for bivariate and multivariate interpolation and approximation’, SIAM J. Numer. Anal. 8, 158–177 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  9. W. J. Gordon and C. A. Hall, “Construction of Curvilinear Co-ordinate Systems and Applications to Mesh Generation”, Int. J. for Numer. Methods in Enng. 7, 461–477 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  10. W. J. Gordon and C. A. Hall, ‘Transfinite element methods: Blending-function interpolation over curved element domains’, Numerishe Mathematik 21, 109–129 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  11. C. A. Hall and B. A. Mutafelija, “Transfinite Interpolation of Steam Tables” J. Computational Physics 18, 79–91 (1975).

    Article  MathSciNet  Google Scholar 

  12. P. Morse and H. Feshbach, Methods of Theoretical Physics, Pt. I, McGraw-Hill, New York, 1953.

    MATH  Google Scholar 

  13. C. J. de la Vallee Poussin, Cours d’Analyse Infinitesimale, Vol. I, Gauthier-Villars, Paris, 1926.

    MATH  Google Scholar 

  14. D. S. Watkins and P. Lancaster, “Some Families of Finite Elements”, J. Inst. Math. Appl. 19, 385–397 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  15. O. C. Zienkiewicz and D. V. Phillips, ‘An automatic mesh generation scheme for plane and curved surfaces by “isoparametric” coordinates’, Int. J. Num. Meth. Engg. 3, 519–528 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  16. O. C. Zienkiewicz, The Finite Element Method in Engineering Science, McGraw-Hill, New York, 1971.

    MATH  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). Vector-Valued Polynomial and Spline Approximation. 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_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-9443-0_3

  • 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