A partially randomized extended Kaczmarz method for solving inconsistent rank-deficient linear systems

Key Points

• The method effectively solves inconsistent linear systems, improving convergence.
• Key evidence shows faster convergence rates in iterative algorithms compared to traditional methods.
• Analysis involves a novel application of the Kaczmarz method to rank-deficient cases for enhanced efficiency.
• Supports the idea that new algorithmic approaches may enable better solutions in complex mathematical settings.