Theme: Numerical Linear Algebra
Course Title: Large Scale Matrix Problems

Lecturer: Dr Linda Stals

Course Content
What does data compression and image recognition have in common? How does different soil composition affect the flow of a liquid? How much water can the dam hold before it bursts? The common tool needed to address these problems and countless more arising in industry and academia is the solution of large scale matrix problems. Some estimates say that 70% of supercomputer time is spent on the solution of such large problems.

The techniques that we are most familiar with cannot be applied to these large systems. For example, suppose it takes 1 second to solve a 100 x 100 sized matrix using Gaussian Elimination, then a quick analysis based on the number of operations implies that it would take about 11.5 days to solve a 10000 x 10000 sized matrix.

In this course, we will introduce new solution techniques to deal with these large-scale problems. We will focus on the solution of linear system of equations using iterative methods. We will introduce the nomenclature used to measure the efficiency and accuracy of these method. We shall define and develop the theoretical properties of the algorithms and then determine their practical use by studying their stability.

Background Reading

  • Numerical Linear Algebraby Lloyd N. Trefethen and David Bau III (SIAM, 1997)
  • Applied Numerical Linear Algebraby James W. Demmel (SIAM, 1997)