Conjugate gradient method regularized

The iterative procedure for the solution of the inverse problem by the regular conjugate gradient method was performed assuming the functions T(x,y), AT(x,y), X(x,y), and J x) are available at the -th iteration. The wall heat flux, q(x), at step n+1 is obtained from... 

This method uses the same ideas as the conventional conjugate gradient method. However, the iteration process is based on the calculation of the regularized steepest descent directions ... 

A numerical scheme for 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... 

II of this book, can be applied to gravity and magnetic inversion. As an illustration, we will show in this section how the conjugate gradient method, outlined in Chapter 5, works in this case. At the same time, we will use gravity field inversion to demonstrate the importance of the regularization technique in the solution of the inverse problems. 

The re-weighted and regularized conjugate gradient method in the space of weighted model parameters, (5.152), discussed in Chapter 5 will be used. This method includes weighting of the model parameters, which forms a very important part of... 

Figure 7-7 illustrates the focusing inversion result obtained by the re-weighted regularized conjugate gradient method. The plots of the misfit and parametric functionals are shown in the top panel of Figure 7-7. In this case the data fitting after 50 iterations is within 4% nevertheless the inverse image adec uately reconstructs the true model. We can clearly recognize two bodies in this image, and the densities correspond well to the true model.

Let us describe, for example, the algorithm based on the regularized conjugate gradient method (5.92), which we reproduce here with small modifications ... 

The regularized conjugate gradient method for solving linear inverse problem equations... 

In order to accelerate the convergence, we apply the regularized conjugate gradient method described by the following iteration process ... 

We can use the re-weighted regularized conjugate gradient method, introduced in Chapter 5, for solving the system of the linear equations (10.96). 

One can use a parabolic line search also (Fletcher, 1985) to improve the convergence rate of the regularized conjugate gradient (RCG) method. 

---