Course - Numerical Analysis HT24

Created: January 11, 2024 | Updated: December 04, 2025 | Read markdown | About these notes | View in context | Study these flashcards

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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.
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^U. Computing the eigenvalues of a matrix reduces to finding the roots of the characteristic polynomial. Because of the Abel-Ruffini 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
• Lecture Notes
  • Lecture 1, Lagrange Interpolation
  • Lecture 2, Gaussian Elimination and LU Factorisation
  • Lecture 3, QR Factorisation
  • Lecture 4, Least-squares problem
  • Lecture 5, SVD
  • Lecture 6, Matrix eigenvalues
  • Lecture 7, Computing eigenvalues
  • Lecture 8, Computing eigenvalues
  • Lecture 9, Best approximation in Inner-product spaces
  • Lecture 10, Orthogonal polynomials
  • Lecture 11, Gauss quadrature
  • Lecture 12, Initial value problems
  • Lecture 13, Initial value problems
  • Lecture 14, Runge-Kutte methods
  • Lecture 15, Multistep methods
  • Lecture 16, Multistep methods
• My notes here are based on the lecture notes and slides above, written by the course lecturer Prof. Yuji Nakatsukasa.
• Overlaps with: Course - Machine Learning MT23^U
• Other courses this term: Courses HT24^U

Notes

• Notes - Numerical Analysis HT24, Misc^U
• Notes - Numerical Analysis HT24, LU decomposition^U
• Notes - Numerical Analysis HT24, Gerschgorin’s theorems^U
• Notes - Numerical Analysis HT24, Givens rotations^U
• Notes - Numerical Analysis HT24, Householder reflectors^U
• Notes - Numerical Analysis HT24, Hermite interpolation^U
• Notes - Numerical Analysis HT24, Tridiagonal matrices^U
• Notes - Numerical Analysis HT24, Schur decomposition^U
• Notes - Numerical Analysis HT24, Singular value decomposition^U
• Notes - Numerical Analysis HT24, Eigenvalues^U
• Notes - Numerical Analysis HT24, Power method^U
• Notes - Numerical Analysis HT24, QR algorithm^U

• Notes - Numerical Analysis HT24, QR decomposition^U

• Notes - Numerical Analysis HT24, Best approximation in inner product spaces^U
• Notes - Numerical Analysis HT24, Lagrange interpolation^U
• Notes - Numerical Analysis HT24, Least-squares^U
• Notes - Numerical Analysis HT24, Orthogonal polynomials^U

• Notes - Numerical Analysis HT24, Quadrature^U

• Notes - Numerical Analysis HT24, Initial value problems^U
• Notes - Numerical Analysis HT24, Multi-step methods^U
• Notes - Numerical Analysis HT24, One-step methods^U
• Notes - Numerical Analysis HT24, Runge-Kutta methods^U

Problem Sheets

• Sheet 1
• Sheet 2
• Sheet 3
• Sheet 4

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