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A homotopy method for parameter estimation of nonlinear differential equations with multiple optima. (English) Zbl 1398.65340
The behavior of the solutions to various nonlinear systems of differential equations strongly depend on some uncertain and unknown parameters involved. The author uses the polynomial chaos approach to quantify the effects of such uncertainties and to generate a set of sampling points which converge to different optimal values of parameters. The homotopy continuation method is then used in order to compute all the solutions of polynomial systems and to estimate the multiple optimal parameter values. Some numerical experiments are carried out in order to underline the efficiency and the accuracy of the proposed method.

MSC:
65P20 Numerical chaos
65H10 Numerical computation of solutions to systems of equations
65K10 Numerical optimization and variational techniques
65F99 Numerical linear algebra
Software:
Bertini
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