MRM solution of the Euler equation

Wc outline now the computational scheme for finding the solution of the Euler equation based on the MRM techniciue. Using notation (4.101) and assuming that f — d d, we can rewrite the iterative process (4.7) - (4.13) as follows 

ihe reguhu ized MRM algorithm for tlu ill-posed in ( rse problem (4.1) solution can bo summarized as follows  

VV e can also apply the steepest dc.scent algorithm (4.52) to the regulari/erl linear inverse pioblem solution. In this ca.se wc have to minimize the parametric functional 

Aftplying the variational o])crator to the last cqtiation, wc find the minimum condition (see cxanqtlc 84 from Ajtpendix D for comparison)  

This new modification of the regularized minimal residual algorithm for the linear inverse problem can be summarized as follows  

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