Secant-type methods and nondiscrete induction

作者：Argyros Ioannis K^*; Hilout Said

来源：Numerical Algorithms, 2012, 61(3): 397-412.

DOI：10.1007/s11075-012-9540-7

• Secant-type methods
• Banach space
• Nondiscrete mathematical induction
• Semilocal convergence
• Traub%26apos
• s method
• Consistent approximation
• Rate of convergence

The celebrated nondiscrete mathematical induction has been used to improve error bounds of distances involved in the discrete case but not the sufficient convergence conditions for Secant-type methods. We show that using the same information as before, the following advantages can be obtained: weaker sufficient convergence conditions; tighter error bounds on the distances involved and a more precise information on the location of the solution. Numerical examples validating the theoretical conclusions are also provided in this study.

• 出版日期2012-11