A note on Kaczmarz algorithm with remotest set control sequence
Provides a theoretical guarantee for a selection rule in the Kaczmarz algorithm, relevant to algebraic reconstruction in tomography.
The paper analyzes the Kaczmarz algorithm with remotest set control, proving that for underdetermined full row rank systems in tomography, each row index is selected at least once during iterations.
In this paper we analyse the Kaczmarz projection algorithm with remotest set control of projection indices. According to this procedure, in each iteration the projection index is one which gives the maximal absolute value of the corresponding residual. We prove that for underdetermined full row rank systems and under some assumptions valid for problems arising in algebraic reconstruction of images in computerized tomography, this selection procedure has the property that each row index is selected at least once during the Kaczmarz algorithm iterations.