  For solving large-scale consistent linear system, we combine two efficient
row index selection strategies with Kaczmarz-type method with oblique
projection, and propose a greedy randomized Kaczmarz method with oblique
projection (GRKO) and the maximal weighted residual Kaczmarz method with
oblique projection (MWRKO) . Through those method, the number of iteration
steps and running time can be reduced to a greater extent to find the
least-norm solution, especially when the rows of matrix A are close to linear
correlation. Theoretical proof and numerical results show that GRKO method and
MWRKO method are more effective than greedy randomized Kaczmarz method and
maximal weighted residual Kaczmarz method respectively.
