Finding good starting points for solving equations by Newton's method
DOI:
https://doi.org/10.33993/jnaat381-897Keywords:
Newton's method, Banach space, Newton-Kantorovich theorem/hypothesis, Fréchet-derivative, Lipschitz, center-Lipschitz conditions, good starting points for Newton's methodAbstract
We study the problem of finding good starting points for the semilocal convergence of Newton's method to a locally unique solution of an operator equation in a Banach space setting. Using a weakened version of the Newton-Kantorovich theorem we show that the procedure suggested by Kung [6] is improved in the sense that the number of Newton-steps required to compute a good starting point can be significantly reduced (under the same computational cost required in the Newton--Kantorovich theorem [3], [5]).Downloads
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