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Avoiding the computation of the second Fréchet-derivative in the convex acceleration of Newton's method

✍ Scribed by J.A. Ezquerro; M.A. Hernández

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
501 KB
Volume
96
Category
Article
ISSN
0377-0427

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✦ Synopsis

We introduce a new two-step method to approximate a solution of a nonlinear operator equation in a Banach space. An existence-uniqueness theorem and error estimates are provided for this iteration using Newton-Kantorovich-type assumptions and a technique based on a new system of recurrence relations. For a special choice of the parameter involved we use, our method is of fourth order.

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