Abstract
Given the data (X_i,y_i), i=1 ,2,...,m, this paper discusses a method to find the values of the linear and nonlinear parameter a and b which minimize the nonlinear functional m Σ^m_i[ Σ^p_<j=1>f_j(b,x_i)a_j - y_i]^2 over aεR^p,bεR^q where m ≧ p + q . By introducing a real parameter, this problem is imbedded into a one-parameter family of problems. Then, a method is presented for solving it by following its solution path using Davidenko's continuation methods. In the course of iterations, the original problem containing p + q + 1 variables is transformed into a problem with q + 1 nonlinear variables by taking the separable structure of the problem into account. By doing so, the new method reduces to solving a series of equations of smaller size and a considerable saving in the storage is obtained. Results of numerical experiments are reported to demonstrate the effectiveness of the proposed method.
