Standard kantorovich theorem of the chebyshev method on complex plane

Abstract

We redefine the Chebyshev method in the equivalent form. Then we use analysis techniques which we have already developed in a series of our research works [1, 2, 3, 4, 5, 6] to establish a Kantorovich type convergence theorem. Also, a lower and an upper bound is clearly given under the standard Kantorovich assumptions for Newton's method.

Keywords:

• Nonlinear complex equations
• complex roots
• standard kantorovich type convergence
• lower and upper error bounds

C.R. Categories:

• 5.1
• 5.15