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