Matrix computations are the primary component of many scientific computations. This year's course will focus on the SVD decomposition and on techniques for sparse matrices. The SVD decomposition is the standard tool for handling least squares problems and discussing sensitivity to problem uncertainty. We will explore ways to improve the speed of the algorithm beyond that of currently available libraries.
Sparse problems involve matrices with many variables but rather few nonzero entries.
Currently developed techniques allow problems of size 100K or so to be solved on PCs. A 1M by 1M problem wth 10M nonzero entries would arise for example in a 3-D grid with 100 grid points in each direction. We will experiment with a publically available numeric library, using and analysing a variety of preconditioners and solvers. The main language used will be Matlab. The course should be accessible and useful to graduate students from CS, from engineering disciplines and to math graduate students.