The SVD-A method uses the concept of the SVD to reformulate the inversion problem in a way that it can be solved with much less numerical effort. The SVD first identifies those combinations of parameters which are uniquely estimable on the basis of the current calibration data set and defines them as super parameters. SVD-A creates and run a new PEST setup based on super parameters instead of base parameters.
When calculating finite-difference derivatives of model outputs with respect to parameters, it actually calculates these derivatives with respect to the super parameters rather than the native model parameters (base parameters). Hence only as many model runs are required per iteration as there are dimensions in the solution space (i.e. number of super parameters).
This method is of fundamental importance for the pilot point method, as it allows calibration and predictive error analysis of highly parametrized models (e.g., using 1000+ parameters) with reasonable effort.
Further reading: PEST Manual (5th Ed.), Chapter 8.5: SVD-Assist.