Skip to main content

Five lectures on the algorithmic aspects of approximation theory

  • 276 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1129)

Keywords

  • Banach Space
  • Approximation Theory
  • Convex Banach Space
  • Compact Hausdorff Space
  • Minimal Projection

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. I. Barrodale, M.J.D. Powell, and F.D.K. Roberts, "The differential correction algorithm for rational approximation", SIAM J. Numer. Analysis 9(1972), 493–504.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. S.N. Dua and H.L. Loeb, "Further remarks on the differential correction algorithm", SIAM J. Numer. Analysis 10(1973), 123–126.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. E.W. Cheney and H.L. Loeb, "Two new algorithms for rational approximation", Numer. Math. 3(1961), 72–75.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. E.W. Cheney and H.L. Loeb, "On rational Chebyshev approximation", Numer. Math. 4(1962), 124–127.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. C.M. Lee and F.D.K. Roberts, "A comparision of algorithms for rational l approximation", Math. Comp. 27(1973), 111–121.

    MathSciNet  MATH  Google Scholar 

  6. E.H. Kaufman, S.F. McCormick, and G.D. Taylor, "An adaptive differential correction algorithm", J. Approx. Theory 37(1983), 197–211.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. E.W. Cheney, "Introduction to Approximation Theory", Chelsea Publishing Co., New York, 1981.

    MATH  Google Scholar 

References

  1. von Neumann, "Functional Operators", vol. II. Princeton 1950.

    Google Scholar 

  2. C. Franchetti and W.A. Light, "On the von Neumann algorithm in Hilbert space", Texas A&M University Report 32 (1982).

    Google Scholar 

  3. F. Deutsch, "The alternating method of von Neumann", in "Multivariate Approximation Theory", ed. by W. Schempp and K. Zeller, Birkhauser 1979.

    Google Scholar 

  4. J.B. Baillon, R.E. Bruck, and S. Reich, "On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces", Houston J. Math. 4(1978), 1–9, MR57 #13590.

    MathSciNet  MATH  Google Scholar 

References

  1. S. Diliberto and E. 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. MR13-334.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. M. Golomb, "Approximation by functions of fewer variables" in "On Numerical Approximation", R.E. Langer, editor. University of Wisconsin Press 1959, pp. 275–327. MR21#962.

    Google Scholar 

  3. G. Aumann, "Uber approximative Nomographie. I". Bayer. Akad. Wiss. Math.-Nat. Kl. S.-B. 1958, 137–155. MR22#1101. Part II, ibid, 1959, 103–109. MR22#6968. Part III, ibid, 1960, 27–34. MR24#B1289.

    Google Scholar 

  4. W. A. Light and E. W. Cheney, "Approximation Theory in Tensor Product Spaces", Lecture Notes in Mathematics, Springer-Verlag, New York. To appear.

    Google Scholar 

  5. J. R. Respess and E. W. Cheney, "Best approximation problems in tensor product spaces", Pacific J. Math. 102(1982), 437–446.

    CrossRef  MathSciNet  MATH  Google Scholar 

References

  1. V.M. Zamyatin, "Chebyshev centers in the space C(S)", First Scientific Conference of Young Scholars of the Akygei, 1971, pp. 28–35.

    Google Scholar 

  2. C. Franchetti and E.W. Cheney, "Simultaneous approximation and restricted Chebyshev centers in function spaces", in "Approximation Theory and Applications", ed. by Z. Ziegler. Academic Press 1981.

    Google Scholar 

  3. R.B. Holmes, "A Course on Optimization and Best Approximation", Lecture Notes in Mathematics, vol. 257, Springer-Verlag, 1972.

    Google Scholar 

  4. D. Amir and Z. Ziegler, "Construction of elements of the relative Chebyshev center", in "Approximation Theory and Applications", ed. by Z. Ziegler. Academic Press 1981.

    Google Scholar 

  5. D. Amir and Z. Ziegler, "Relative Chebyshev centers in normed linear spaces", parts I and II. J. Approximation Theory.

    Google Scholar 

  6. D. Amir, J. Mach, Saatkamp, "Existence of Chebyshev centers", Trans. American Math. Soc. 271(1982), 513–524.

    MathSciNet  MATH  Google Scholar 

  7. P.W. Smith and J.D. Ward, "Restricted centers in C(ω)", Proc. Amer. Math. Soc. 48(1975), 165–172.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Cheney, E.W. (1985). Five lectures on the algorithmic aspects of approximation theory. In: Turner, P.R. (eds) Numerical Analysis Lancaster 1984. Lecture Notes in Mathematics, vol 1129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075156

Download citation

  • DOI: https://doi.org/10.1007/BFb0075156

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15234-7

  • Online ISBN: 978-3-540-39412-9

  • eBook Packages: Springer Book Archive