Skip to main content

Best approximation in tensor product spaces

  • Conference paper
  • First Online:
Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 773))

Work supported in part by the U. S. Army Scientific Research Office at The University of Texas, Austin, Texas, U.S.A.

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 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Schatten, Robert, "A Theory of Cross-spaces," Annals of Mathematics Studies, No. 26, Princeton University Press, Princeton, 1950.

    MATH  Google Scholar 

  2. Robertson, A.P., and Wendy Robertson, "Topological Vector Spaces," Cambridge University Press, Cambridge, 1964.

    MATH  Google Scholar 

  3. Schaeffer, H. H., "Topological Vector Spaces," MacMillan Company, New York, 1966.

    Google Scholar 

  4. Gordon, W. J., "Blending-function methods of bivariate and multivariate interpolation and approximation," General Motors Research Laboratories, Report 834, October 1968.

    Google Scholar 

  5. Diliberto, S. P., and E. G. Straus, "On the approximation of a function of several variables by the sum of functions of fewer variables," Pacific J. Math. 1 (1951), 195–210.

    Article  MathSciNet  MATH  Google Scholar 

  6. Fulkerson, D. R., and P. Wolfe, "An algorithm for scaling matrices," SIAM Review 4 (1962), 142–146.

    Article  MathSciNet  MATH  Google Scholar 

  7. Bank, R., "An automatic scaling procedure for a d’Yakanov-Gunn iteration scheme," CNA Report 142, University of Texas at Austin, August 1978. To appear, Linear Algebra and Its Applications.

    Google Scholar 

  8. Bank, R., and D. J. Rose, "Marching algorithms for elliptic boundary value problems I: The constant coefficient case," SIAM J. on Numerical Analysis 14 (1977), 792–829.

    Article  MathSciNet  MATH  Google Scholar 

  9. Bank, R., "Marching algorithms for elliptic boundary value problems II: The variable coefficient case," SIAM J. on Numerical Analysis 14 (1977), 950–970.

    Article  MathSciNet  MATH  Google Scholar 

  10. Settari, A., and K. Aziz, "A generalization of the additive correction methods for the iterative solution of matrix equations," SIAM J. on Numerical Analysis 10 (1973), 506–521.

    Article  MathSciNet  MATH  Google Scholar 

  11. v. Golitschek, M., "An algorithm for scaling matrices and computing the minimum cycle mean in a digraph," preprint, August 1979, Institute for Applied Mathematics, University of Würzburg, Germany.

    MATH  Google Scholar 

  12. v. Golitschek, M., "Approximation of functions of two variables by the sum of two functions of one variable," preprint, August 1979, Institute for Applied Mathematics, University of Würzburg, Germany.

    Google Scholar 

  13. Rothblum, U. G., and H. Schneider, "Characterizations of optimal scalings of matrices," Report RS 2678 (1978), Yale University, New Haven.

    MATH  Google Scholar 

  14. Hammerlin, G., and L. L. Schumaker, "Procedures for kernel approximation and solution of Fredholm integral equations of the second kind," CNA Report 1 8, University of Texas at Austin, November 1977.

    Google Scholar 

  15. Atkinson, K., "A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind," SIAM, Philadelphia, 1976.

    MATH  Google Scholar 

  16. Phillips, G. M., J. H. McCabe, E. W. Cheney, "A mixed-norm bivariate approximation problem with applications to Lewanowicz operators," pp. 315–323 in "Multivariate Approximation," D.C. Handscomb, ed., Academic Press, New York, 1978. Also CNA Report 127, University of Texas at Austin, October 1977.

    Google Scholar 

  17. Krabs, W., "Optimierung und Approximation," B. G. Teubner, Stuttgart, 1975 (particularly Sec. 5.3).

    Book  MATH  Google Scholar 

  18. Atlestam, B., and F. E. Sullivan, "Iteration with best approximation operators," Rev. Roumaine Math. Puras Appl. 21 (1976), 125–131. MR 53#6188.

    MathSciNet  MATH  Google Scholar 

  19. Sullivan, F. E., "A generalization of best approximation operators," Ann. Mat. Pura Appl. 107 (1975), 245–261. MR 53#3564.

    Article  MathSciNet  MATH  Google Scholar 

  20. Aumann, G., "Uber Approximative Nomographie II," Bayer. Akad. Wiss. Math. Nat. Kl. S.B. 1959, 103–109. MR 22#6968.

    Google Scholar 

  21. Light, W. A., and E. W. Cheney, "On the approximation of a bivariate function by the sum of univariate functions," to appear, J. Approximation Theory. Also CNA Report 140, University of Texas at Austin, August 1978.

    Google Scholar 

  22. Kelley, C. T., "A note on the approximation of functions of several variables by sums of functions of one variable," Report 1873, Math. Research Center, Madison, Wisconsin, August 1978.

    Google Scholar 

  23. Dyn, R., "A straightforward generalization of Diliberto and Straus’ algorithm does not work," to appear, J. Approximation Theory. Report dated December 1978, Math. Research Center, Madison, Wisconsin.

    Google Scholar 

  24. Light, W. A., J. H. McCabe, G. M. Phillips, and E. W. Cheney, "The approximation of bivariate functions by sums of univariate ones using the L-1 metric," Report CNA 147, University of Texas at Austin, March 1979.

    Google Scholar 

  25. Golomb, M., "Approximation by functions of fewer variables," pp. 275–327 in "On Numerical Approximation," R. E. Langer, ed., University of Wisconsin Press, 1959.

    Google Scholar 

Download references

Authors

Editor information

G. Alistair Watson

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Cheney, E.W. (1980). Best approximation in tensor product spaces. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094161

Download citation

  • DOI: https://doi.org/10.1007/BFb0094161

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09740-2

  • Online ISBN: 978-3-540-38562-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics