On the Solution of Constrained and Weighted Linear Least Squares Problems

Important problems in many scientific computational areas are least squares problems. The problem of constraint least squares with full column weight matrix is a class of these problems. In this presentation, we are concerned with the connection between the condition numbers and the rounding error in the solution of the problem of constrained and weighted linear least squares. The fact that this problem is an intrinsic feature of least squares problems makes it necessary to study the characteristics of its solution. Investigation of the theoretical characteristics of the solution of our problem is based on perturbing the problem and driving bounds for the relative error. Explicit expressions for the inverse and Moore-Penrose inverse are used to estimate these bounds. Moreover, the effects of weights are presented. AMS classification: Primary 65F15; Secondary 65G05