The solution of large-scale least-squares problems on supercomputers

The paper discusses methods for solving medium to large-scale sparse least-squares problems on supercomputers, illustrating the present remarks by experiments on the CRAY-2 supercomputer at Harwell. The method it is primarily concerned with is an augmented system approach which has the merit of both robustness and accuracy, in addition to a kernel operation that is just the solution of a symmetric indefinite sysem. The paper considers extensions to handle weighted and constrained problems, and includes experiments on systems similar to those arising in the Karmarkar algorithm for linear programming. It indicates how recent improvements to the kernel software could greatly improve the performance of the least-squares code.