Least‐squares problems for Michaelis–Menten kinetics |
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| Authors: | K. P. Hadeler Dragan Jukić Kristian Sabo |
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| Affiliation: | 1. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, U.S.A.;2. Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek HR‐31 000, CroatiaDepartment of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek HR‐31 000, Croatia===;3. Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek HR‐31 000, Croatia |
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| Abstract: | The Michaelis–Menten kinetics is fundamental in chemical and physiological reaction theory. The problem of parameter identification, which is not well posed for arbitrary data, is shown to be closely related to the Chebyshev sum inequality. This inequality yields sufficient conditions for existence of feasible solutions both for nonlinear and for linear least‐squares problems. The conditions are natural and practical as they are satisfied if the data show the expected monotone and concave behaviour. Copyright © 2007 John Wiley & Sons, Ltd. |
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| Keywords: | Michaelis– Menten kinetics nonlinear least‐squares problem existence Chebyshev sum inequality |
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