algorithm: SOLA by elimination of theconstraint (Lanczos bidiagonalization)

1.-3.

These steps are similar to Algorithm 2.3 (click here), except that is kept in factored form.

4.

For each of the q columns of , apply steps of the LSQR algorithm to produce the solutions

5.

Compute the estimates of f and the corresponding variances at

6.

If needed, compute the corresponding averaging kernels

 

Changing the target functions requires re-computing steps 4 through 6. In this variant of the algorithm the k acts as the regularization parameter; increasing k requires additional steps of the LSQR algorithm to be computed in step 4. If k is decreased no extra Lanczos iterates are needed, provided the iteration vectors are saved. In any case steps 5 through 6 need to be re-computed.