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.