Supplementary projections for the acceleration of Kaczmarz algorithm

When solving a linear least squares problem using the classical Kaczmarz solver, usually different accelerating techniques are employed. We study a method of adding to the original problem supplementary directions for projection as linear combinations of rows or columns. In order to conserve the sparsity pattern of the system matrix we propose an algorithm which computes an initial transformation via clustering based on the sparsity similarity. Numerical experiments show that, as the number of clusters is increased, the acceleration is decreased.