Block AOR iterative schemes for large-scale least-squares problems

The problem of accelerating the convergence rate of iterative schemes, as they apply to the solution of large-scale least-squares problems by means of different splittings, is addressed here. New convergence results, together with explicit expressions for the optimal factors and their corresponding spectral radii, are derived for certain schemes from the block Accelerated Overrelaxation (AOR) family. It is shown that, for a class of least-squares problems, the proposed optimal block iterative scheme converges unconditionally and asymptotically faster than the optimal block Successive Overrelaxation (SOR) method, while in all other cases the two schemes are competitive. Numerical examples are used to illustrate our results.

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