Computing

, Volume 62, Issue 2, pp 163–178

Partial Linearization of One Class of the Nonlinear Total Least Squares Problem by Using the Inverse Model Function

  • D. Jukič
  • R. Scitovski
  • H. Späth

Abstract.

In this paper we consider a special nonlinear total least squares problem, where the model function is of the form \(f(x;a,b)=\phi^{-1}(ax+b)\). Using the fact that after an appropriate substitution, the model function becomes linear in parameters, and that the symmetry preserves the distances, this nonlinear total least squares problem can be greatly simplified. In this paper we give the existence theorem, propose an efficient algorithm for searching the parameters and give some numerical examples.

AMS Subject Classifications:65D10, 62J02. 
Key words.Nonlinear total least squares, errors in variables, orthogonal least squares fitting. 

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Copyright information

© Springer Verlag, Wien, 1999

Authors and Affiliations

  • D. Jukič
    • 1
  • R. Scitovski
    • 2
  • H. Späth
    • 3
  1. 1.Department of Mathematics, Faculty of Food Technology, F. Kuhača 18, HR-31000 Osijek, Croatia, e-mail: jukicd@oliver.efos.hr HR
  2. 2.Department of Mathematics, Faculty of Electrical Engineering, Istarska 3, HR-31\,000 Osijek, Croatia, e-mail: scitowsk@drava.etfos.hr HR
  3. 3.Fachbereich Mathematik, Carl von Ossietzky Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany, e-mail: spaeth@mathematik.uni-oldenburg.de DE

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