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Solving Separable Nonlinear Least Squares Problems by Davidenko's Method

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ABSTRACT

SOLVING SEPARABLE NONLINEAR LEAST SQUARES

PROBLEMS BY DA VIDENKO'S METHOD

Nobuko Sagara Aichi University

Given the data (x.,

y.),

i=1,2, ... ,m, this paper discusses a method to

~ ~

find the values of the linear and nonlinear parameters a and b which minimize the nonlinear functional

over a e: ~, be: Rq 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 sepa-rable 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 effec-tiveness of the proposed method.

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