Unified Treatment of Regula Falsi, Newton--Raphson, Secant, and Steffensen Methods for Nonlinear Equations
Regula falsi, Newton--Raphson, secant, and Steffensen methods are four very effective numerical procedures used for solving nonlinear equations of the form f(x) = 0. They are derived via linear interpolation procedures. Their analyses can be carried out by making use of interpolation theory through divided differences and Newton's interpolation formula. In this note, we unify these analyses. The analysis of the Steffensen method given here seems to be new and is especially simpler than the standard treatments. The contents of this note should also be a useful exercise/example in the application of polynomial interpolation and divided differences in introductory courses in numerical analysis.
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Published May, 2006
Copyright © 2006 by Avram Sidi