Geodesic
Suitability of linearization of nonlinear problems not only in biology and medicine
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 171-188

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Biology and medicine are not the only fields that present problems unsolvable through a linear models approach. One way to overcome this obstacle is to use nonlinear methods, even though these are not as thoroughly explored. Another possibility is to linearize and transform the originally nonlinear task to make it accessible to linear methods. In this aricle I investigate an easy and quick criterion to verify suitability of linearization of nonlinear problems via Taylor series expansion so that linear models with type II constraints could be used.
Biology and medicine are not the only fields that present problems unsolvable through a linear models approach. One way to overcome this obstacle is to use nonlinear methods, even though these are not as thoroughly explored. Another possibility is to linearize and transform the originally nonlinear task to make it accessible to linear methods. In this aricle I investigate an easy and quick criterion to verify suitability of linearization of nonlinear problems via Taylor series expansion so that linear models with type II constraints could be used.
Classification : 62F30, 62H12, 62H99, 62J02, 62J05, 65C60
Keywords: Linear models with constraints; compartmental analysis; nonlinear models; linearization via a Taylor series 
Vrbková, Jana. Suitability of linearization of nonlinear problems not only in biology and medicine. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 171-188. http://geodesic.mathdoc.fr/item/AUPO_2009_48_1_a14/
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[1] Kubáček, L., Kubáčková, L.: Statistics and Metrology. Vyd. Univ. Palackého, Olomouc, 2000 (in Czech).

[2] Fišerová, E., Kubáček, L., Kunderová, P.: Linear Statistical Models, Regularity and Singularities. Academia, Praha, 2007.

[3] Rao, C. R., Mitra, S. K.: Generalized Inverse of Matrices and its Applications. J. Wiley, New York–London–Sydney–Toronto, 1971. | MR | Zbl

[4] Hagiwara, M., Rusinek, H., Lee, V. S., Losada, M., Bannan, M. A., Krinsky, G. A., Taouli, B.: Advanced Liver Fibrosis: Diagnosis with 3D Whole-Liver Perfusion MR Imaging?Initial Experience. Radiology 246 (2008), 926–934.

[5] Holčík, J.: Modelování a simulace biologických systémů. ČVUT, Praha, 2006 (in Czech).