Schröder's Method

Two families of equations used to find roots of nonlinear functions of a single variable. The ``B'' family is more robust andcan be used in the neighborhood of degenerate multiple roots while still providing a guaranteed convergence rate. Almost allother root-finding methods can be considered as special cases of Schröder's method. Householder humorously claimed thatpapers on root-finding could be evaluated quickly by looking for a citation of Schröder's paper; if the reference weremissing, the paper probably consisted of a rediscovery of a result due to Schröder (Stewart 1993).

One version of the ``A'' method is obtained by applying Newton's Method to ,

References

Householder, A. S. The Numerical Treatment of a Single Nonlinear Equation. New York: McGraw-Hill, 1970.

Scavo, T. R. and Thoo, J. B. ``On the Geometry of Halley's Method.'' Amer. Math. Monthly 102, 417-426, 1995.

Schröder, E. ``Über unendlich viele Algorithmen zur Auflösung der Gleichungen.'' Math. Ann. 2, 317-365, 1870.

Stewart, G. W. ``On Infinitely Many Algorithms for Solving Equations.'' English translation of Schröder's original paper. College Park, MD: University of Maryland, Institute for Advanced Computer Studies, Department of Computer Science, 1993. ftp://thales.cs.umd.edu/pub/reports/imase.ps.

• Lemniscate of Gerono
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