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In this paper, an extension of Kaczmarz method, the Kaczmarz method withoblique projection (KO), is introduced and analyzed. Using this method, anumber of iteration steps to solve the over-determined systems of linearequations are significantly reduced, and the the computing time is much saved,especially for those problems that contain some linear equations withnear-linear correlation. Simultaneously, a randomized version--randomizedKaczmarz method with oblique projection (RKO) is established. The convergenceproofs of these two methods are given and numerical experiments show theeffectiveness of the two methods for uniformly distributed random data.Especially when the system has correlated rows, the improvement of experimentalresults is very prominent.

On Kaczmarz method with oblique projection for solving large overdetermined linear systems