Model-space preconditioning

The technique is based on a post-multiplication of the matrix $\bold L$ by the diagonal matrix ${\bf C^{-1}}$.

The preconditioning operator introduces a new model $\bold x$ given by

$$\bold x = \bold C \bold m \EQNLABEL{mod-prec}$$ (15)

By the preconditioning transformation, we have recast the original inversion relation equ1 into

$$\bold d = \bold L \bold C^{-1} \bold x. \EQNLABEL{prec}$$ (16)

After solving for $\bold x$ we easily compute $\bold m = \bold C^{-1} \bold x$.