A Deterministic Kaczmarz Algorithm for Solving Linear Systems
A Deterministic Kaczmarz Algorithm for Solving Linear Systems
We propose a new deterministic Kaczmarz algorithm for solving consistent linear systems $A\mathbf{x}=\mathbf{b}$. Basically, the algorithm replaces orthogonal projections with reflections in the original scheme of Stefan Kaczmarz. Building on this, we give a geometric description of solutions of linear systems. Suppose $A$ is $m\times n$, we show that the …