, Volume 8, Issue 3, pp 181–184 | Cite as

Average linear least squares regression

  • H. Späth


We describe an algorithm and a corresponding FORTRAN subroutine for finding a regression vectorx withn components such that
$$F(x) = \sum\limits_{i = 1}^s {w_i \left\| {A_i x - b_i } \right\|}$$
is minimized, where ∥.∥ denotes the Euclidean norm,W i >0,A i are design matrices withm i rows andn columns, andb i are observation vectors withm i components (i=1,...,s).


Euclidean Norm Observation Vector Design Matrice FORTRAN Subroutine 


Wir beschreiben einen Algorithmus und eine zugehörige FORTRAN-Subroutine zur Auffindung einesn-komponentigen Parametervektorsx derart daß
$$F(x) = \sum\limits_{i = 1}^s {w_i \left\| {A_i x - b_i } \right\|}$$
minimiert wird, wobei ∥.∥ die Euklidische Norm bezeichnet,W i >0,A i Versuchsmatrizen mitm i Zeilen undn Spalten undb i Beobachtungsvektoren der Längem i (i= 1,...,s)sind.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Eckhardt U (1975) On an optimization problem related to minimal surfaces with obstacles. In: Bulirsch R, Oettli W, Stoer J (eds) Optimization and optimal control. Springer, Berlin Heidelberg New YorkGoogle Scholar
  2. 2.
    Eckhardt U (1980) Weber's problem and Weiszfeld's algorithm in general spaces. Math Progr 18:186–196Google Scholar
  3. 3.
    Lawson CL, Hanson RL (1974) Solving least squares problems. Prentice Hall, Englewood CliffsGoogle Scholar
  4. 4.
    Overton ML (1983) A quadratically convergent method for minimizing a sum of Euclidean norms. Math Progr 27:34–63Google Scholar
  5. 5.
    Späth H (1985) Cluster dissection and analysis, theory, FORTRAN programs, examples. Horwood, ChichesterGoogle Scholar
  6. 6.
    Voss H, Eckhardt U (1980) Linear convergence of generalized Weiszfeld's method. Computing 25:243–251Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • H. Späth
    • 1
  1. 1.Fachbereich MathematikUniversität OldenburgOldenburgF. R. Germany

Personalised recommendations