After notes on Chebyshev’s iterative method

Abstract

This paper is a small review of Chebyshev’s method. The geometric interpretation as a generalization of Newton’s method is derived. Using this interpretation its global convergence is proved. Some dynamical properties are studied. As a higher order method, they are more complicated than in Newton’s method. Finally, some applications are revisited pointing out the advantages of Chebyshev’s method with respect Newton’s method.

Keywords

• nonlinear equations
• chebyshev’s iterative method
• geometric interpretation
• global convergence
• dynamics
• applications
• 65j15