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 problems recursively stems from the need for fast real-time signal processing strategies. The computational cost of least-squares solvers can also limit the applicability of this technique in geophysical problems. We have considered a recursive least-squares solution for least-squares wave equation migration with sliding windows involving several fixed rank downdating and updating computations. This technique can be applied for dynamic and stationary processes. If we use enough data in each windowed setup, the spectrum of the preconditioned system is clustered around one and the method will converge superlinearly with probability one. Numerical experiments were performed to test the effectiveness of the technique for least-squares migration.

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