| Course Description
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.
- Norms and floating-point arithmetic.
- Cholesky factorization and symmetric positive definite
- LU factorization and general linear systems.
- Toeplitz 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.
- Theory of matrix eigenvalue problems.
- QR algorithm and the inverse power method for eigenvalue
- The Lanczos algorithm for large sparse symmetric eigenvalue problems.
- Conjugate-gradient method for large sparse symmetric
positive definite linear systems.
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.