  Recursive estimates of large systems of equations in the context of least
squares fitting is a common practice in different fields of study. For example,
recursive adaptive filtering is extensively used in signal processing and
control applications. The necessity of solving least squares problem via
recursive algorithms comes from the need of fast real-time signal processing
strategies. Computational cost of using least squares algorithm could also
limits the applicability of this technique in geophysical problems. In this
paper, we consider recursive least squares solution for wave equation least
squares migration with sliding windows involving several rank K downdating and
updating computations. This technique can be applied for dynamic and stationary
processes. One can show that in the case of stationary processes, the spectrum
of the preconditioned system is clustered around one and the method will
converge superlinearly with probability one, if we use enough data in each
windowed setup. Numerical experiments are reported in order to illustrate the
effectiveness of the technique for least squares migration.
