On Solving Some Large Linear Problems: By Direct Methods

Abstract

A general scheme for obtaining approximations bar(x) to x = A^* b where A^* is the pseudo-inverse of A is proposed. It is shown that if the computations are performed without rounding errors then bar(x)=x. It is demonstrated how some well known and commonly used special methods can be found from the general scheme. In the case where A is large and sparse we give some general rules which often lead to a considerable reduction of the computing time and/or the storage needed and to an improved accurary. The efficiency of the suggesed general rules is illustrated by numerical results.