A General Updating Algorithm for Constrained Linear Least Squares Problems

Abstract

Linear least squares problems which are sparse except for a small subset of dense equations can be efficiently solved by an updating method. Often the least squares solution is also required to satisfy a set of linear constraints, which again can be divided into sparse and dense subsets. This paper develops an updating algorithm for the solution of such problems. The algorithm is completely general in that no restrictive assumption on the rank of any subset of equations or constraints is made.