The focus of this research is on the solution of sparse least squares problems on sequential and parallel computers. An important problem of interest will be the solution of equality constrained least squares problems, or as they are often posed, equality constrained minimization problems. Three different approaches will be examined: (1) Null Space Methods, (2) Iterative Solution of the Kuhn- Tucker Equations, and (3) Weighted Least Squares Methods. The methods will be considered from the standpoints of error analysis, computational complexity, and adaptability to high performance architectures. Graph theoretical issues arise in the investigation of the null space approach to equality constrained least squares, and solution of sparse least squares problems. In particular, the Dulmage-Mendelsohn decomposition of a rectangular matrix will play a role in the computational aspects of all the problems considered.
