Advertisement

Numerische Mathematik

, Volume 32, Issue 4, pp 439–459 | Cite as

On the convergence of an algorithm for discreteLp approximation

  • Jerry M. Wolfe
Article

Summary

The convergence properties of an algorithm for discreteLp approximation (1≦p<2) that has been considered by several authors are studied. In particular, it is shown that for 1<p<2 the method converges (with a suitably close starting value) to the best approximation at a geometric rate with asymptotic convergence constant 2-p. A similar result holds forp=1 if the best approximation is unique. However, in this case the convergence constant depends on the function to be approximated.

Subject Classifications

AMS(MOS) 65D15 CR 5.13 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fletcher, R.J., Grant, A., Hebden, M.D.: The Calculation of Linear BestL p Approximations. Computer J.14, 226–279 (1971)Google Scholar
  2. 2.
    Kahng, S.W.: BestL p Approximation. Math. of Comp.26, 505–508 (1972)Google Scholar
  3. 3.
    Cheney, E.W.: Introduction to Approximation Theory. New York: McGraw-Hill 1966Google Scholar
  4. 4.
    Barrodale, I., Roberts, F.D.K.: Applications of Mathematical Programming tol p Approximation. In: Nonlinear Programming, J.B. Rosen, O. Mangasarian, K. Ritter, eds., pp. 447–464. New York: Academic Press 1970Google Scholar
  5. 5.
    Goldstein, A.A.: Constructive Real Analysis. New York: Harper and Row 1967Google Scholar
  6. 6.
    Merle, G., Spath, H.: Computational Experience with DiscreteL p Approximation. Computing12, 315–321 (1974)Google Scholar
  7. 7.
    Ekblom, H.: Calculation of Linear BestL p Approximation. BIT13, 292–300 (1973)Google Scholar
  8. 8.
    Rice, J.: The Approximation of Functions Vol. 1: Linear Theory. Reading Mass.: Addison-Wesley 1964Google Scholar
  9. 9.
    Watson, G.: On Two Methods for DiscreteL p-Approximation. Computing,18, 263–266 (1977)Google Scholar
  10. 10.
    Gentleman, W.M.: Robust Estimation of Multivariate Location by Miniminizing PTH Power Deviations. Thesis, Princeton University, (1965)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Jerry M. Wolfe
    • 1
  1. 1.Department of MathematicsUniversity of OregonEugeneUSA

Personalised recommendations