Two families of equations used to find roots of nonlinear functions of a single variable. The "B" family is more robust and can be used in the neighborhood of degenerate multiple roots while still providing a guaranteed convergence rate. Almost all other root-finding methods can be considered as special cases of Schröder's method. Householder humorously claimed that papers on root-finding could be evaluated quickly by looking for a citation of Schröder's paper; if the reference were missing, 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 ,
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. Monthly102, 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. http://citeseer.nj.nec.com/93609.html.
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![x_(n+1)=x_n-(f(x_n)f^'(x_n))/([f^'(x_n)]^2-f(x_n)f^('')(x_n))](/images/equations/SchroedersMethod/NumberedEquation1.svg)
