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MATH0058 - Lecture Notes

Welcome to MATH0058

Fundamentals

Matrix and vector norms
Floating Point Arithmetic
Principles of backward error analysis
Backward error and condition number of linear systems of equations
A quick survey of the \(\mathcal{O}\) -notation
Memory layout and Numpy arrays

LU Decomposition and its numerical stability

Solving linear system with the LU Decomposition
Backward error of the LU decomposition and pivoting
Backward error of the LU decomposition
Implementing the LU decomposition in Python

Orthogonal decompositions

The QR Decomposition
The Singular Value decomposition
Least Squares Problems

Eigenvalue problems

Complex vector spaces
Basic properties of eigenvalue problems
The Schur decomposition
Perturbation results for eigenvalue problems
Computing eigenvalues

Interpolation and quadrature

Introduction to interpolation
Numerical quadrature
Stable quadrature schemes

Self Check Questions

Week 1 Self check questions and solutions
Week 2 Self check questions and solutions
Week 3 Self check questions and solutions
Week 4 Self check questions and solutions
Week 5 Self check questions and solutions
Week 6 Self check questions and solutions
Week 7 Self check questions and solutions
Week 8 Self check questions and solutions
Week 9 Self check questions and solutions

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By Timo Betcke
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