BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-78-697
       ENTRY:: June 22, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: On the linear least squares problem with a quadratic
               constraint
        TYPE:: Technical Report
      AUTHOR:: Gander, Walter
        DATE:: November 1978
       PAGES:: 62
    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.
       NOTES:: [Adminitrivia V1/Prg/19950622]
         END:: STAN//CS-TR-78-697