The convergence of new second-order iterative methods are analyzed in Banach spaces by introducing a system of recurrence relations. A system of a priori error bounds for that method is also provided. The methods are defined by using a constant bilinear operator A , instead of the second Fréchet derivative appearing in the defining formula of the Chebyshev method. Numerical evidence that the methods introduced here accelerate the classical Newton iteration for a suitable A is provided.
Applied Mathematics and Optimization – Springer Journals
Published: Apr 1, 2025
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