Linear Algebra is a central and widely applicable part of Mathematics.
It is estimated that many (if not most) computers in the world are
computing with matrix algorithms at any moment in time whether these
be embedded in visualization software in a computer game or calculating
prices for some financial option. This course builds on elementary
linear algebra and in it we derive, describe and analyse a number of
widely used constructive methods (algorithms) for various problems
involving matrices.
Only elementary linear algebra is assumed in this course.
The part A Numerical Analysis course would be helpful, indeed some swift review and extensions of some of the material of that course is included here.
Numerical Methods for solving linear systems of equations, computing eigenvalues and singular values and various related problems involving matrices are the main focus of this course.
Common problems in linear algebra. Matrix structure, singular value decomposition.
QR factorization, the QR algorithm for eigenvalues.
Direct solution methods for linear systems, Gaussian elimination and its variants.
Iterative solution methods for linear systems.
Chebyshev polynomials and Chebyshev semi-iterative methods, conjugate gradients, convergence analysis, preconditioning.
