A new type of recurrence relations for the secant method^∗

Supported in part by a grant of the DGES (PB-96-0120-C03-02) and a grant of the University of La Rioja API-98/B12.

Abstract

We apply the Secant method to solve nonlinear operator equations in Banach spaces. We establish a Newton-Kantorovich convergence theorem using a new system of recurrence relations and give an explicit expression for the a priori error bounds. Moreover, we apply our results to the numerical resolution of a nonlinear boundary value problem of second order and improve the error bounds obtained by other authors.

Keywords:

• The Secant method
• recurrence relations
• a priori error bounds

ASM Classifications:

• 65J15
• 47H17

C.R. Categories:

• G.1.5

Supported in part by a grant of the DGES (PB-96-0120-C03-02) and a grant of the University of La Rioja API-98/B12.

Supported in part by a grant of the DGES (PB-96-0120-C03-02) and a grant of the University of La Rioja API-98/B12.

Notes

Supported in part by a grant of the DGES (PB-96-0120-C03-02) and a grant of the University of La Rioja API-98/B12.