论文信息 - Avoiding the computation of the second Fre´chet-derivative in the convex acceleration of Newton's method

Avoiding the computation of the second Fre´chet-derivative in the convex acceleration of Newton's method

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.

José Antonio Ezquerro | J. A. Ezquerro | M. A. Hernández

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