Conjugate Gradient Method for TLS

The Rayleigh Quotient can be minimized by iterative techniques. Zhu et al. (1997) introduced a method based on conjugate gradients (CG) to solve the TLS problem which was adapted from the earlier work of Chen et al. (1986). I implemented this CG-based algorithm and present pseudocode in Appendix A.

Theory guarantees that the CG method converges in n steps, where n is the size of the model vector. However, in practical situations with real seismic data, a ``useful'' model may appear after relatively few (<< n) CG iterations. How useful the model and how few the iterations depends on the problem. Nonetheless, in practice, the computational cost and memory requirements are nearly always much less with CG than with SVD.