next up previous print clean
Next: OPPORTUNITIES FOR SMART DIRECTIONS Up: PRECONDITIONING THE REGULARIZATION Previous: Statistical interpretation

The preconditioned solver

Summing up the ideas above, we start from fitting goals  
 \begin{displaymath}
\begin{array}
{lll}
\bold 0 &\approx& \bold F \bold m \ -\ \bold d \\ \bold 0 &\approx& \bold A \bold m\end{array}\end{displaymath} (8)
and we change variables from $\bold m$ to $\bold p$ using $\bold m = \bold A^{-1} \bold p$ 
 \begin{displaymath}
\begin{array}
{llllcl}
\bold 0 &\approx & \bold F \bold m \ ...
 ...d 0 &\approx & \bold A \bold m &=& \bold I & \bold p\end{array}\end{displaymath} (9)
Preconditioning means iteratively fitting by adjusting the $\bold p$ variables and then finding the model by using $\bold m = \bold A^{-1} \bold p$.A new reusable preconditioned solver is the module solver_prc [*]. Likewise the modeling operator $\bold F$ is called Fop and the smoothing operator $\bold A^{-1}$ is called Sop. Details of the code are only slightly different from the regularized solver solver_reg [*]. solver_prcPreconditioned solver
next up previous print clean
Next: OPPORTUNITIES FOR SMART DIRECTIONS Up: PRECONDITIONING THE REGULARIZATION Previous: Statistical interpretation
Stanford Exploration Project
4/27/2004