Testing Numerical Methods Solving the Linear Least Squares Problem


The paper derives a general method for testing algorithms solving the Least-Squares-Problem (LS-Problem) of a linear equation system. This test method includes the generation of singular test matrices with arbitrary condition, full column rank and exactly representable generalized inverses, as well as a method for choosing general right hand sides. The method is applied to three LS-Problem solvers in order to assess under what conditions the error in the least squares solution is only linearly dependent on the condition number.


Condition Number Generalize Inverse Test Matrice Full Column Rank Diploma Thesis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Greville, T.N.E.: Some Applications of the Pseudoinverse of a Matrix. SIAM Rev. 2, 485–494 (1943)MathSciNetGoogle Scholar
  2. 2.
    Lawson, C.L., Hanson, R.J.: Solving Least Squares Problems. Prentice Hall, New Jersey (1974)MATHGoogle Scholar
  3. 3.
    Peters, G., Wilkinson, J.H.: The Least-Squares Problem and Pseudoinverses. Comput. J. 13, 309–316 (1970)MATHCrossRefGoogle Scholar
  4. 4.
    Rice, J.R.: Experiments on Gram-Schmidt Orthogonalization. Math. Comput. 20, 325–328 (1966)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    v.d. Sluis, A.: Stability of the Solutions of Linear Least Squares Problems.Num. Mathematik 23, 241–254 (1975)CrossRefGoogle Scholar
  6. 6.
    Weihs, C.: Kondition des linearen Ausgleichsverfahrens, Testmatrizen, Ver-gleich von Lösungsverfahren. Diploma thesis, Universität Bonn (1977)Google Scholar
  7. 7.
    Zielke, G.: Testmatrizen mit maximaler Konditionszahl. Computing 13, 33–54(1974)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Zielke, G.: Report on Test Matrices for Generalized Inverses. Computing 36,105–162 (1986)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 2009

Authors and Affiliations

  1. 1.Fakultät StatistikTechnische Universität DortmundDortmundGermany

Personalised recommendations