Regularized solution in the Backus-Gilbert method

The matrix column of the unknown coefficients can now be found based on the minimization of the Tikhonov parametric functional  

the column vector of theoretical data d for the given model m (ro) can be determined, according to expression (3.113), by the formula  

Now we should calculate the first variation of the parametric functional with respect to the perturbation of the parameters 

Comparing (3.130) with (3.11G), wc can see now that vc have to invei t tlie well-conditioned matrix F -f al rather than tlic possibly ill-conditioned matrix F. Substituting (3.130) into (3.125), wc write 

oniparing (3.131) and (3.119) we see that, in the case of the regularized solution we invc rt tht- well-conditioned matrix (F + f)I) instead of ill-conditioned F. which makes our rc sult staljkr 

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