Research in Numerical Linear Algebra and Numerical Methods for Large-Scale Least Squares and Other Problems.

摘要

The research problems studied for the U. S. Army Research Office over the six year period of these grants are each in the research area of Numerical Linear Algebra and Applications. The objectives of the research were to develop new techniques for handling large-scale problems which involve interative or direct methods for solving large sparse systems of linear equations or least squares problems. The topics to be studied included: (1) the convergence of iterative methods for solving systems of linear equations, (2) hyperbolic systems of partial differential equations, (3) large-scale least squares computations, (4) M-matrices and related topics on nonegativity, (5) the computation of stationary distributions for Markov chains and (6) sparse matrix computations in structural optimization. Research on these topics was to be coordinated with associated scientists and engineers from some of the application areas such as queueing network analysis, compartmental analysis of biological systems, geodetic adjustment methods and structural analysis. Some theoretical research was to be done and certain algorithms and software were to be developed and tested on real problems from these areas.