The preconditioning operator in this example is a diagonal weighting matrix, but any operator may be used as a preconditioner, the choice depends on the application. Often a preconditioner is chosen to speed up an inversion Karrenbach (1994), though here the weighting matrix is chosen to impart a desired property to the model.
In a manner analogous to weighting the model, the residual can be weighted. This results in a problem formulated as Nichols (1994)
|Wd = WHm.||(5)|
Ji's 1994 approach is similar to preconditioning, in that he applies an iterative reweighting to the model space. However, it is not applied as a change of variables. That is, the weighting is not reapplied to the final solution. This approach is like defining a new operator