Minimization in the space of weighted parameters

The minimization problem (5.117) can be reformulated using a space of weighted parameters  

We can consider a forward operator, which relates the new weighted parameters m to the weighted data  

Using these notations, we can rewrite the parametric functional (5.117) as 

Therefore, the minimization problem (5.132) is equivalent to the minimization of the same parametric functional as in formula (5.117). Note, however, that the unknown parameters are now weighted model parameters, in . In order to obtain the original model parameters we have to apply inverse weighting to the result of minimization of the parametric functional (5.132)  

Numerical experiments show that, as a rule, the iterative process converges faster for (5.132) than for (5.117). The minimization method in the space of weighted parameters is similar to the RRCG method described above. 

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