Yao et al. (1999) and Berryman (2001b) provide methods for calculating the a posteriori covariance for iterative methods based on SVD. For a thorough description of the methods I refer to these papers. The principle is as follows;
each iteration provides one extra vector in the solution space. After *K* iterations these *K* vectors are used for calculating the a posteriori covariance. As a consequence, if more iterations are performed, not only the approximated inverse but also the a posteriori covariance becomes more accurate.
Figure 9b,c shows a posteriori covariance matrices for *M*=33 model parameters obtained by respectively CG and LSQR. Both matrices resemble the real a posteriori covariance matrix (Fig.9a).
Note that both methods compute the complete covariance matrix, so also the non diagonal elements.

9/18/2001