Preconditioning

The preconditioned solver

Summing up the ideas above, we start from fitting goals

$$\begin{array}{lll} \bold 0 &\approx& \bold F \bold m - \bold d \bold 0 &\approx& \bold A \bold m \end{array}$$ (8)

and we change variables from $\bold m$ to $\bold p$ using $\bold m = \bold A^{-1} \bold p$

$$\begin{array}{llllcl} \bold 0 &\approx & \bold F \bold m -\... ... 0 &\approx & \bold A \bold m &=& \bold I & \bold p \end{array}$$ (9)

Preconditioning means iteratively fitting by adjusting the $\bold p$ variables and then finding the model by using $\bold m = \bold A^{-1} \bold p$ .