Root Finding in one Dimension

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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

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