Root Finding in one Dimension

Subject classification: this is a mathematics resource.

Summary

This course belongs to the track Numerical Algorithms in the Department of Scientific Computing in the School of Computer Science.

In this course, students will learn how to solve problems of the type $f(x)=0\,\;$ numerically. Convergence rates, termination criteria and implementation details are discussed.

Introduction

• Why do we want to solve $f(x)=0\,\;$?
• Why do we want to solve it numerically?
• Formal definition of the problem.
• Maybe a bit of history?

Binomial Search

• Derivation
• The Algorithm
• Convergence

Secant Method

• Derivation
• The Algorithm
• Convergence
• Iterative form

Iterative Methods

• $x_{n+1}=F(x_{n})\,\;$
• Convergence rates

Newton's Method

• Derivation
• The Algorithm
• Convergence

Halley's Method

• Derivation
• The Algorithm
• Convergence
• Generalization