Residual statics corrections can be formulated as a linear inverse problem. Usually, solving this problem involves a large ill-posed matrix inverse calculation. Therefore, a fast algorithm that can handle the ill-posed problem is needed in practice. In this paper, the least-squares QR factorization (LSQR), based on Lanczos and QR factorization, is presented. This method works on rectangular matrix and is a rapidly converging and stable algorithm for the ill-posed problem.
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