In this work, we obtain a semilocal convergence result for the secant method in Banach spaces under mild convergence conditions. We consider a condition for divided differences which generalizes those usual ones, i.e., Lipschitz continuous and Holder continuous conditions. Also, we obtain a result f
Exact order of convergence of the secant method
β Scribed by M. Raydan
- Publisher
- Springer
- Year
- 1993
- Tongue
- English
- Weight
- 486 KB
- Volume
- 78
- Category
- Article
- ISSN
- 0022-3239
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π SIMILAR VOLUMES
Newton's method Divided difference Recurrence relations a b s t r a c t We introduce a three-step Chebyshev-Secant-type method (CSTM) with high efficiency index for solving nonlinear equations in a Banach space setting. We provide a semilocal convergence analysis for (CSTM) using recurrence relatio
Let f : C β C have a multiple zero Ξ± with integer multiplicity m β₯ 1 and be analytic in a sufficiently small neighborhood of Ξ±. For parameter-controlled Newton-secant method defined by we investigate the maximal order of convergence and the theoretical asymptotic error constant by seeking the relat