# 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 ${\displaystyle f(x)=0\,\;}$ numerically. Convergence rates, termination criteria and implementation details are discussed.

## Introduction

• Why do we want to solve ${\displaystyle f(x)=0\,\;}$?
• 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

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

## Newton's Method

• Derivation
• The Algorithm
• Convergence

## Halley's Method

• Derivation
• The Algorithm
• Convergence
• Generalization