𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the global convergence of Chebyshev's iterative method

✍ Scribed by S. Amat; S. Busquier; J.M. Gutiérrez; M.A. Hernández

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
132 KB
Volume
220
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

In [A. Melman, Geometry and convergence of Euler's and Halley's methods, SIAM Rev. 39(4) (1997) 728-735] the geometry and global convergence of Euler's and Halley's methods was studied. Now we complete Melman's paper by considering other classical third-order method: Chebyshev's method. By using the geometric interpretation of this method a global convergence theorem is performed. A comparison of the different hypothesis of convergence is also presented.

📜 SIMILAR VOLUMES

On the semilocal convergence of efficien
On the semilocal convergence of efficient Chebyshev–Secant-type methods
✍ I.K. Argyros; J.A. Ezquerro; J.M. Gutiérrez; M.A. Hernández; S. Hilout 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 257 KB

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