| Course Description
To provide an introduction to the fundamental ideas of matrix computations.
It emphasizes the design, analysis, and computer implementation
of accurate and efficient algorithms and the sensitivity analysis of
basic matrix problems.
- Norms and floating-point arithmetic.
- Cholesky factorization and symmetric positive definite
linear systems of equations.
- LU factorization and general linear systems of equations.
- Sensitivity of problems and numerical stability of algorithms.
- Blocking algorithms for higher performance.
- QR factorization and linear least squares problems.
- Singular value decomposition.
- Eigenvalue problems - theory and computations
- Iterative methods for large sparse linear systems (including classic iterative methods
and Krylov subspace methods with focus on the conjugate gradient method)
- Tensor decomposition (if we have time available).
Prerequisites: Facility with a high level
programming language such as MATLAB, Python, and a good
introductory matrix theory course. Previous experience of numerical
computations is also important, such as COMP 350 or MATH 317.
Some assignments will be done by using MATLAB.