# Course - Numerical Analysis HT24

> Source: https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/ · Updated: 2025-12-04 · Tags: uni, course

> Introduces some topics in numerical analysis, which is roughly the study of finding approximate solutions to continuous problems in mathematics. Topics include: solving systems of linear equations, calculating eigenvalues, approximating functions with polynomials, and computing solutions to ODEs.
> <br>
> Why do you need approximate solutions rather than exact ones? There are many reasons, but one particular example comes up in [Notes - Numerical Analysis HT24, Eigenvalues](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/eigenvalues/). Computing the eigenvalues of a matrix reduces to finding the roots of the characteristic polynomial. Because of the [Abel-Ruffini theorem](https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem), there is no way of writing down these roots in simple terms and so you have to use approximate methods to find them.

- [Course Webpage](https://courses.maths.ox.ac.uk/course/view.php?id=4962)
- Lecture Notes
	- [Lecture 1, Lagrange Interpolation](https://courses.maths.ox.ac.uk/pluginfile.php/93886/mod_resource/content/1/lect1_Lagrange.pdf)
	- [Lecture 2, Gaussian Elimination and LU Factorisation](https://courses.maths.ox.ac.uk/pluginfile.php/93887/mod_resource/content/1/lect2_GELU.pdf)
	- [Lecture 3, QR Factorisation](https://courses.maths.ox.ac.uk/pluginfile.php/93888/mod_resource/content/1/lect3_QR.pdf)
	- [Lecture 4, Least-squares problem](https://courses.maths.ox.ac.uk/pluginfile.php/93889/mod_resource/content/1/lect4_least_squares.pdf)
	- [Lecture 5, SVD](https://courses.maths.ox.ac.uk/pluginfile.php/93890/mod_resource/content/1/lect5_SVD.pdf)
	- [Lecture 6, Matrix eigenvalues](https://courses.maths.ox.ac.uk/pluginfile.php/93891/mod_resource/content/1/lect6_eig.pdf)
	- [Lecture 7, Computing eigenvalues](https://courses.maths.ox.ac.uk/pluginfile.php/93892/mod_resource/content/1/lect7and8_QR.pdf)
	- [Lecture 8, Computing eigenvalues](https://courses.maths.ox.ac.uk/pluginfile.php/93892/mod_resource/content/1/lect7and8_QR.pdf)
	- [Lecture 9, Best approximation in Inner-product spaces](https://courses.maths.ox.ac.uk/pluginfile.php/93893/mod_resource/content/1/lect9_Hilbert.pdf)
	- [Lecture 10, Orthogonal polynomials](https://courses.maths.ox.ac.uk/pluginfile.php/93894/mod_resource/content/1/lect10_orthpoly.pdf)
	- [Lecture 11, Gauss quadrature](https://courses.maths.ox.ac.uk/pluginfile.php/93895/mod_resource/content/1/lect11_Gauss.pdf)
	- [Lecture 12, Initial value problems](https://courses.maths.ox.ac.uk/pluginfile.php/93896/mod_resource/content/1/lect12and13_ivps1.pdf)
	- [Lecture 13, Initial value problems](https://courses.maths.ox.ac.uk/pluginfile.php/93896/mod_resource/content/1/lect12and13_ivps1.pdf)
	- [Lecture 14, Runge-Kutte methods](https://courses.maths.ox.ac.uk/pluginfile.php/93897/mod_resource/content/1/lect14_rk.pdf)
	- [Lecture 15, Multistep methods](https://courses.maths.ox.ac.uk/pluginfile.php/93898/mod_resource/content/1/lect15and16_multistep.pdf)
	- [Lecture 16, Multistep methods](https://courses.maths.ox.ac.uk/pluginfile.php/93898/mod_resource/content/1/lect15and16_multistep.pdf)
- My notes here are based on the lecture notes and slides above, written by the course lecturer [Prof. Yuji Nakatsukasa](https://people.maths.ox.ac.uk/nakatsukasa/).
- Overlaps with: [Course - Machine Learning MT23](https://ollybritton.com/notes/uni/part-a/mt23/machine-learning/)
- Other courses this term: [Courses HT24](https://ollybritton.com/notes/uni/part-a/ht24/courses/)

### Notes
- [Notes - Numerical Analysis HT24, Misc](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/misc/)
- [Notes - Numerical Analysis HT24, LU decomposition](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/lu-decomposition/)
- [Notes - Numerical Analysis HT24, Gerschgorin's theorems](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/gerschgorins-theorems/)
- [Notes - Numerical Analysis HT24, Givens rotations](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/givens-rotations/)
- [Notes - Numerical Analysis HT24, Householder reflectors](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/householder-reflectors/)
- [Notes - Numerical Analysis HT24, Hermite interpolation](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/hermite-interpolation/)
- [Notes - Numerical Analysis HT24, Tridiagonal matrices](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/tridiagonal-matrices/)
- [Notes - Numerical Analysis HT24, Schur decomposition](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/schur-decomposition/)
- [Notes - Numerical Analysis HT24, Singular value decomposition](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/singular-value-decomposition/)
- [Notes - Numerical Analysis HT24, Eigenvalues](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/eigenvalues/)
- [Notes - Numerical Analysis HT24, Power method](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/power-method/)
- [Notes - Numerical Analysis HT24, QR algorithm](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/qr-algorithm/)
- [Notes - Numerical Analysis HT24, QR decomposition](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/qr-decomposition/)

- [Notes - Numerical Analysis HT24, Best approximation in inner product spaces](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/best-approximation-in-inner-product-spaces/)
- [Notes - Numerical Analysis HT24, Lagrange interpolation](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/lagrange-interpolation/)
- [Notes - Numerical Analysis HT24, Least-squares](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/least-squares/)
- [Notes - Numerical Analysis HT24, Orthogonal polynomials](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/orthogonal-polynomials/)
- [Notes - Numerical Analysis HT24, Quadrature](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/quadrature/)

- [Notes - Numerical Analysis HT24, Initial value problems](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/initial-value-problems/)
- [Notes - Numerical Analysis HT24, Multi-step methods](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/multi-step-methods/)
- [Notes - Numerical Analysis HT24, One-step methods](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/one-step-methods/)
- [Notes - Numerical Analysis HT24, Runge-Kutta methods](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/runge-kutta-methods/)

### Problem Sheets
- [Sheet 1](https://courses.maths.ox.ac.uk/pluginfile.php/93882/mod_assign/introattachment/0/NA_sheet1.pdf)
- [Sheet 2](https://courses.maths.ox.ac.uk/pluginfile.php/93883/mod_assign/introattachment/0/NA_sheet2.pdf)
- [Sheet 3](https://courses.maths.ox.ac.uk/pluginfile.php/93884/mod_assign/introattachment/0/NA_sheet3.pdf)
- [Sheet 4](https://courses.maths.ox.ac.uk/pluginfile.php/93885/mod_assign/introattachment/0/NA_sheet4.pdf)

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