Single projection Kaczmarz extended algorithms - Petra, Stefania; Popa, Constantin (Numerical algorithms, 2016)
In order to find the least squares solution of a very large and inconsistent system of equations, one can employ the extended Kaczmarz algorithm. This method simultaneously removes the error term, so that a consistent system is asymptotically obtained, and applies Kaczmarz iterations for the current approximation of this system. It has been shown that for random corrections of the right hand side and Kaczmarz updates selected at random, the algorithm converges to the least squares solution. In this work we consider deterministic strategies like the maximal-residual and the almost-cyclic control, and show convergence to a least squares solution.
Gesehen am 15.03.2018