# Part IB - Numerical Analysis

## Lectured by G. Moore, Lent 2016

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

This is an HTML version of the notes, generated using some horribly-written scripts and pdf2htmlEX. These are not guaranteed to display well, but do let me know if something is broken. Note however that I cannot help you if your browser does not support standard HTML features (eg. this part is known not to work well with w3m). You can either view all sections in a single page (Full version), or access individual sections below. If you want to download a pdf, head to the Notes page.

# Contents

- V Full version
- 0 Introduction
- 1 Polynomial interpolation
- 1.1 The interpolation problem
- 1.2 The Lagrange formula
- 1.3 The Newton formula
- 1.4 A useful property of divided differences
- 1.5 Error bounds for polynomial interpolation
- 2 Orthogonal polynomials
- 2.1 Scalar product
- 2.2 Orthogonal polynomials
- 2.3 Three-term recurrence relation
- 2.4 Examples
- 2.5 Least-squares polynomial approximation
- 3 Approximation of linear functionals
- 4 Expressing errors in terms of derivatives
- 5 Ordinary differential equations
- 6 Stiff equations
- 7 Implementation of ODE methods
- 8 Numerical linear algebra
- 9 Linear least squares