Kaczmarz method with oblique projection

The popular randomized Kaczmarz method is a single random orthogonal projection method. In this paper, a single randomized Kaczmarz method with oblique projection is discussed. A sufficient condition for the monotone convergence of the Kaczmarz method with oblique projection is given. Choosing an appropriate oblique projection direction, the convergence of Kaczmarz method with oblique projection will be greatly accelerated. At the same time, the convergence rate of Kaczmarz method with oblique projection along this direction is given. Numerical experiments show the effectiveness of Kaczmarz method with oblique projection.