A new family of exponential iteration methods with quadratic convergence of both diameters and points for enclosing zeros of nonlinear equations

✍ Scribed by Jinhai Chen

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 209 KB
• Volume: 45
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/j.mcm.2006.07.003

✦ Synopsis

This paper presents a new class of exponential iteration methods with global convergence for finding a simple root x * of a nonlinear equation f (x) = 0 in the interval [a, b]. The new methods are shown to be quadratically convergent. Both the sequences of diameters {b na n } and the iterative sequence {x nx * } are quadratically convergent to zero. The theoretical analysis and numerical experiments show that new exponential iterative formulae are effective and comparable to those of the well-known Newton and Steffensen methods.