On the convergence and optimal error estimates of king's iteration procedures for solving nonlinear equations

Abstract

In this paper we deal with a family of King's iteration procedures for solving nonlinear equations. Under the Ostrowski-Kantorovich conditions, we set up the convergent theorem of iteration procedures. Meanwhile, optimal error estimates are obtained. Finally, conclusions of the theorem are shown by a numerical example.

Keywords:

• Nonlinear equations
• King's multipoint iteration procedures
• optimal error estimate
• Kantorovich convergence theorem

C.R. Categories:

• G.1.5