A direct method for the solution of sparse linear least squares problems

AbstractWe examine a direct method based on an LU decomposition of the rectangular coefficient matrix for the solution of sparse linear least squares problems. We wish to develop a method which is also stable for weighted systems and at the same time preserves much of the original sparsity. We also describe a general updating scheme for modifying the solution when extra equations are added. This is particularly useful in the case when these added equations are nonsparse. We illustrate our description and analyses by runs on test examples