Abstract
A second order iteration method is proposed for the simultaneous computation of a root and its multiplicity of a single nonlinear equation. This method consists essentially in a Steffenson-like acceleration of a Newton-Raphson process that depends on a parameter which is forced to converge to the multiplicity.
Zusammenfassung
Wir stellen ein Itertionsverfahren vor zur gleichzeitigen Berechnung einer Wurzel und seiner Multiplizität einer einzigen nichtlinearen Gleichung. Dieses Verfahren enthält wesentlich eine Steffenson-artige Beschleunigung eines von einem Parameter abhängigen Newton-Raphson-Prozesses, wobei dieser Parameter zwangsmäßig zur Multiplizität konvergiert.
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References
Traub, J. F.: Iterative methods for the solution of equations. Englewood Cliffs, N. J.: Prentice-Hall 1964.
Nesdore, P. F.: The determination of an algorithm which uses the mixed strategy technique for the solution of single nonlinear equations, in: Rabinowitz, P. (ed.): Numerical methods for nonlinear algebraic equations, pp. 27–45. London: Gordon and Breach 1970.
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Van de Vel, H. A method for computing a root of a single nonlinear equation, including its multiplicity. Computing 14, 167–171 (1975). https://doi.org/10.1007/BF02242315
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DOI: https://doi.org/10.1007/BF02242315