Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T10:47:37.555Z Has data issue: false hasContentIssue false
  • English
  • Français

The best least squares approximation problem for a 3-parametric exponential regression model

Published online by Cambridge University Press:  17 February 2009

D. Jukić  and
R. Scitovski
D. Jukić
Affiliation:
University “J. J. Strossmayer”, Faculty of Food Technology, Department of Mathematics, Franje Kuhača 18, 31 000 Osijek, Croatia, email: jukicd@oliver.efos.hr
R. Scitovski
Affiliation:
University “J. J. Strossmayer”, Faculty of Electrical Engineering, Department of Mathematics, Istarska 3, 31 000 Osijek, Croatia, email: scitowsk@drava.etfos.hr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Given the data (pi, ti, fi), i = 1,…,m, we consider the existence problem for the best least squares approximation of parameters for the 3-parametric exponential regression model. This problem does not always have a solution. In this paper it is shown that this problem has a solution provided that the data are strongly increasing at the ends.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 2 , October 2000 , pp. 254 - 266
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Barrodale, I., Roberts, F. D. K. and Hunt, C. R., “Computing best lp approximations by functions nonlinear in one parameter”, Comput. J. 13 (1970) 382–386.CrossRefGoogle Scholar
[2]Demidenko, E. Z., Optimization and regression (in Russian, Nauka, Moscow, 1989).Google Scholar
[3]Golub, G. H. and Pereyra, V., “The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate”, SIAM J. Numer. Anal. 10 (1973) 413–432.CrossRefGoogle Scholar
[4]Jukić, D. and Scitovski, R., “The existence of optimal parameters of the generalized logistic function”, Appl. Math. Comput. 77 (1996) 281–294.Google Scholar
[5]Marušić, M. and Bajzer, Ž., “Generalized two-parameter equation of growth”, J. Math. Anal. Appl. 179 (1993) 446–462.CrossRefGoogle Scholar
[6]Mitrinović, D. S., Pečarić, J. and Fink, A. M., Classical and New Inequalities in Analysis (Kluwer, Dordrecht, 1993).CrossRefGoogle Scholar
[7]Mühlig, H., “Lösung praktischer Approximationsaufgaben durch Parameteridentifikation”, ZAMM 73 (1993) T837–T839.Google Scholar
[8]Osborne, M. R., “Some special nonlinear least squares problems”, SIAM J. Numer. Anal. 12 (1975) 571–592.CrossRefGoogle Scholar
[9]Osborne, M. R. and Smyth, G. K., “A modified Prony algorithm for exponential function fitting”, SIAM J. Sci. Comput. 16 (1995) 119–138.CrossRefGoogle Scholar
[10]Ratkowsky, D. A., Handbook of Nonlinear Regression Models (M. Dekker, New York, 1990).Google Scholar
[11]Rice, J. R., The Approximation of Functions, Vol. 1 (Addison-Wesley, Reading, Massachusetts, 1964).Google Scholar
[12]Rice, J. R., The Approximation of Functions, Vol. 2 (Addison-Wesley, Reading, Massachusetts, 1969).Google Scholar
[13]Ross, G. J. S., Nonlinear Estimation (Springer-Verlag, New York, 1990).CrossRefGoogle Scholar
[14]Rudolph, P. E. and Herrendörfer, G., “Optimal experimental design and accuracy of parameter estimation for nonlinear regression models used in long-term selection”, Biom. J. 37 (1995) 183–190.CrossRefGoogle Scholar
[15]Ruhe, A. and Wedin, P. A., “Algorithms for separable nonlinear least squares problems”, SIAM Review 22 (1980) 318–337.CrossRefGoogle Scholar
[16]Scitovski, R., “A special nonlinear least squares problem”, J. Comput. Appl. Math. 53 (1994) 323–331.CrossRefGoogle Scholar
[17]Scitovski, R. and Jukić, D., “A method for solving the parameter identification problem for ordinary differential equations of the second order” Appl. Math. Comput. 74 (1996) 273–291.Google Scholar
[18]Scitovski, R. and Jukić, D., “Total least squares problem for exponential function”, Inverse Problems 12 (1996) 341–349.CrossRefGoogle Scholar
[19]Späth, H., H, , Numerik (Vieweg, Braunschweig, 1994).CrossRefGoogle Scholar
[20]Varah, J. M., “On fitting exponentials by nonlinear least squares”, SIAM J. Sci. Stat. Comput. 6 (1985) 30–44.CrossRefGoogle Scholar
[21]Varah, J. M., “Relative size of the Hessian terms in nonlinear parameter estimation”, SIAM J. Sci. Stat. Comput. 11 (1990) 174–179.CrossRefGoogle Scholar