Identification on a Manifold of Systems

1 Nonlinear Least Squares 1.1 Nonlinear Least Squares on Euclidean n-space We are interested in minimizing (locally) the following criterion function 4>: R" —• R defined by 1 1 m where ƒ : R " —* R m denotes the residual mapping with corresponding coordinate functions ( the so-called residuals) f' : R " —• R , (i = 1 , . . . , m ) , and || • || denotes the Euclidean norm (on R m ) . We assume ƒ to be a t least iwice continuously differentiable, in order to be able to apply Newton's method for minimization and to compare with it. The associated Jacobian mapping is denoted by J : R n — R m x " and defined in each point x 6 R " byj 'This research was carried out as part of NWO research project 611-304-019. t Address: Free University, Department of Economics and Econometrics, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands. E-mail: [email protected].