𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Improved Newton’s method without direct function evaluations

✍ Scribed by E.N. Malihoutsaki; I.A. Nikas; T.N. Grapsa

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
523 KB
Volume
227
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

a b s t r a c t

For solving systems of nonlinear equations, we have recently developed a Newton's method to manage issues with inaccurate function values or problems with high computational cost. In this work we introduce a modification of the above method, reducing the total computational cost and improving, in general, its overall performance. Moreover, the proposed version retains the quadratic convergence, the good behavior over singular and ill-conditioned cases of Jacobian matrix, and its capability to be ideal for imprecise function problems. Numerical results demonstrate the efficiency of the new proposed method.

📜 SIMILAR VOLUMES

An improvement of convergence in Newton'
An improvement of convergence in Newton's method
✍ S. Lopez 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 393 KB

Newton's method is based on a linear approximation of the function in a neighborhood of a solution point. It can be demonstrated that the error in the current iteration depends on the norm of second derivative. Instead using a higher-order approximation, the second derivative is used here to transfo