Report Number: CS-TR-78-697
Institution: Stanford University, Department of Computer Science
Title: On the linear least squares problem with a quadratic constraint
Author: Gander, Walter
Date: November 1978
Abstract: In this paper we present the theory and practical computational aspects of the linear least squares problem with a quadratic constraint. New theorems characterizing properties of the solutions are given and extended for the problem of minimizing a general quadratic function subject to a quadratic constraint. For two important regularization methods we formulate dual equations which proved to be very useful for the applications of smoothing of datas. The resulting algorithm is a numerically stable version of an algorithm proposed by Rutishauser. We show also how to choose a third order iteration method to solve the secular equations. However we are still far away from a foolproof machine independent algorithm.