PROJECT TITLE :

On the Exponential Convergence of the Kaczmarz Algorithm

ABSTRACT:

The Kaczmarz algorithm (KA) may be a well-liked method for solving a system of linear equations. In this note we derive a new exponential convergence result for the KA. The key allowing us to ascertain the new result's to rewrite the KA in such a approach that its answer path will be interpreted because the output from a explicit dynamical system. The asymptotic stability results of the corresponding dynamical system will then be leveraged to prove exponential convergence of the KA. The new bound is also compared to existing bounds.


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