Least-squares method regularized nonlinear

In a different field of study, namely physics, Macdonald [41 ] successfully applied the Nonlinear Least Squares (NLS) method to invert a ID pure diffusion problem. He applied the method to recover a number of Dirac-delta sources with large measurement errors in the data. Alapati and Kabala [2] employed the NLS method without regularization to recover the release history of a ground-water contaminant plume from its current measured spatial distribution. The closed form solution of Eq. (2) subject to Eqs. (3-5) is [34] ... 

The steepest descent method for nonlinear regularized least-squares inversion To solve the problem of minimization of the parametric functional using the steepest descent method, let us calculate the first variation of P (m,d), assuming that the operator A(m) is differentiable, so that... 

Nonlinear least-squares inversion by the conjugate gradient method This method uses the same ideas as the regularized conjugate gradient method ... 

Using equations (5.102), (5.103), (5.105), and (5.106), we can obtain m iteratively. 5.3.6 The numerical scheme of the regularized conjugate gradient method for nonlinear least-squares vnversion... 

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