Preconditioning

THE PRECONDITIONED SOLVER

Summing up the previous ideas, we start from fitting goals:

$$\begin{array}{lll} \bold 0 &\approx& \bold F \bold m - \bold d \ \bold 0 &\approx& \bold A \bold m \end{array}$$ (15)

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

$$\begin{array}{llllcl} \bold 0 &\approx & \bold F \bold m -\... ... 0 &\approx & \bold A \bold m &=& \bold I & \bold p \end{array}$$ (16)

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