A surrogate hyperplane Kaczmarz method for solving consistent linear equations

Kaczmarz method is a traditional and widely used iterative method for solving consistent linear equations while its randomized version recently attracts much more attention due to its linear convergence rate in expectation. A general scheme of surrogate hyperplane Kaczmarz method is proposed to generate a new hyperplane by combining a number of selected hyperplanes. In particular, the residual-based surrogate hyperplane Kaczmarz method is presented and its convergence rate is studied in details. Numerical experiments further show that the proposed method is efficient and faster than the existing method.