Skip to main content
Log in

A Complex Mean Value Form for Curves

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

A new mean value form for analytic functions defined on curves in the complex plane is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L.V. Ahlfors, Complex Analysis, 3rd ed. (McGraw-Hill, New York, 1979).

    Google Scholar 

  2. G. Alefeld and J. Herzberger, Introduction to Interval Computations (Academic Press, New York, 1983).

    Google Scholar 

  3. O. Caprani and K. Madsen, Mean value forms in interval analysis, Computing 24 (1980) 147–154.

    Google Scholar 

  4. E.R. Hansen, On the centered form, in: Topics in Interval Analysis, ed. E.R. Hansen (Clarendon Press, Oxford, 1969) pp. 102–106.

    Google Scholar 

  5. R. Krawczyk and K. Nickel, Die zentrische Form in der Intervallarithmetik, ihre quadratische Konvergenz und ihre Inklusionsisotonie, Computing 28 (1982) 117–137.

    Google Scholar 

  6. U. Kulisch and W.L. Miranker, Computer Arithmetic in Theory and Practice (Academic Press, New York, 1981).

    Google Scholar 

  7. R.E. Moore, Interval Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1966).

    Google Scholar 

  8. M. Neher, The mean value form for complex analytic functions, Computing 67 (2001) 255–268.

    Google Scholar 

  9. A. Neumaier, Interval Methods for Systems of Equations (Cambridge Univ. Press, Cambridge, 1990).

    Google Scholar 

  10. M.S. Petković and L.D. Petković, The representation of complex circular functions using Taylor series, Z. Angew. Math. Mech. (1981) 661–662.

  11. M.S. Petković and L.D. Petković, Complex Interval Arithmetic and Its Applications (Wiley/VCH, New York, 1998).

    Google Scholar 

  12. L.B. Rall, Mean value and Taylor forms in interval analysis, SIAMJ. Math. Anal. 14 (1983) 223–238.

    Google Scholar 

  13. H. Ratschek and J. Rokne, Computer Methods for the Range of Functions (Ellis Horwood, Chichester, 1984).

    Google Scholar 

  14. J. Rokne, The range of values of a complex polynomial over a complex interval, Computing 22 (1979) 153–169.

    Google Scholar 

  15. J. Rokne, A low complexity explicit rational centered form, Computing 34 (1985) 261–263.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Neher, M. A Complex Mean Value Form for Curves. Numerical Algorithms 37, 337–343 (2004). https://doi.org/10.1023/B:NUMA.0000049479.71077.08

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:NUMA.0000049479.71077.08

Navigation