Weaker convergence conditions for the secant method
نویسندگان
چکیده
منابع مشابه
Convergence Conditions for the Secant Method
We provide new sufficient convergence conditions for the convergence of the Secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, Lipschitz–type and center–Lipschitz–type instead of just Lipschitz–type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise ...
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The Newton–Kantorovich hypothesis (15) has been used for a long time as a sufficient condition for convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space setting. Recently in [3], [4] we showed that this hypothesis can always be replaced by a condition weaker in general (see (18), (19) or (20)) whose verification requires the same computational cos...
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ژورنال
عنوان ژورنال: Applications of Mathematics
سال: 2014
ISSN: 0862-7940,1572-9109
DOI: 10.1007/s10492-014-0054-6