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In this thesis, we present the O(n log^2 n) superfast linear least squares Schur algorithm(ssschur). The algorithm we describe illustrates a fast way of solving linear equations or linear least squares problems with low displacement rank. This algorithm is based on the O(n^2) Schur algorithm, sped up via FFT. The algorithm solves an illconditioned Toeplitzlike system using Tikhonov regularization. The regularized system solved is Toeplitzlike and is of displacement rank, 4. In this thesis, we also show the effect of the choice of the regularization parameter on the quality of the images reconstructed.
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