Abstract
We give a new theorem concerning the convergence of Newton's method to compute an approximate zero of a system of equations. In this result, the constanth 0=0.162434... appears, which plays a fundamental role in the localization of “good” initial points for the Newton iteration. We apply it to the determination of an appropriate discretization of the time interval in the classical homotopy method.
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Communicated by J. Della Dora
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Yakoubsohn, JC. A universal constant for the convergence of Newton's method and an application to the classical homotopy method. Numer Algor 9, 223–244 (1995). https://doi.org/10.1007/BF02141589
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DOI: https://doi.org/10.1007/BF02141589