Abstract
A number of methods that require only function evaluation to find a bracketed root are discussed. The Snyder, Pegasus, and Anderson-Björck schemes of Regula Falsi type converge superlinearly, but all use relatively slow secant steps. Two recent methods are faster because they exploit the rational interpolation step used by Anderson and Björck, and virtually eliminate secant steps.
Zusammenfassung
Mehrere Methoden zur Berechnung einer eingeklammerten Wurzel, die nur die Auswertung einer Funktion verlangen, werden diskutiert. Die Snyder-, Pegasus- und Anderson-Björck-Verfahren von der Regula-Falsi-Art konvergieren superlinear, aber alle benutzen relativ langsame Sekantenschritte. Zwei kürzlich entwickelte Methoden sind schneller, da sie den von Anderson und Björck benutzten rationalen Interpolationsschritt ausnutzen und fast ganz die Sekantenschrite eliminieren.
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Work performed under the auspices of the U.S. Energy Research and Development Administration.
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King, R.F. Methods without secant steps for finding a bracketed root. Computing 17, 49–57 (1976). https://doi.org/10.1007/BF02252259
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DOI: https://doi.org/10.1007/BF02252259