COMP540
Matrix Computations

Course Description

Course Objectives:
To provide students with a strong knowledge and understanding of
the important algorithms in numerical matrix computations, as well
as the difficulties involved in practical implementation and use
of these algorithms. The course also gives students an increased
understanding of the basic problems in the area, together with the
sensitivity of each problem.
Detailed Description:
 Norms and floatingpoint arithmetic.
 Cholesky factorization and symmetric positive definite
linear systems.
 Sensitivity of problems and numerical stability of algorithms.
 Blocking algorithms for higher performance.
 QR factorization and linear least squares problems.
 Singular value decomposition and generalized inverses.
 QR algorithm and inverse power method for eigenvalue
problems.
 Iterative methods for large sparse linear systems (including classic iterative methods,
MINRES, SYMMLQ and Conjugategradient)
Prerequisites: Facility with a high level scientific
programming language such as C, C++, Java, or Fortran, 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.

