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Efficiency of the Multisection Method

J. S. C. Prentice

Abstract

We study the efficiency of the multisection method for univariate nonlinear equations, relative to that for the well-known bisection method. We show that there is a minimal effort algorithm that uses more sections than the bisection method, although this optimal algorithm is problem dependent. The number of sections required for optimality is determined by means of a Lambert W function.

Efficiency of the Multisection Method

Abstract

We study the efficiency of the multisection method for univariate nonlinear equations, relative to that for the well-known bisection method. We show that there is a minimal effort algorithm that uses more sections than the bisection method, although this optimal algorithm is problem dependent. The number of sections required for optimality is determined by means of a Lambert W function.
Paper Structure (6 sections, 19 equations)

This paper contains 6 sections, 19 equations.

Table of Contents

  1. Introduction
  2. Relevant Concepts, Terminology and Notation
  3. Theory
  4. Numerical Calculations
  5. Concluding Comments
  6. Appendix