ISSN:
1432-0606
Keywords:
Key words. Nonlinear equations in Banach spaces, Second-order methods, Newton's method, A priori error bounds. AMS Classification. 47H17, 65J15.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002459911012
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