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JSIAM Letters

The Japan Society for Industrial and Applied Mathematics

In 2015, Gower and Richtárik presented a unifying framework for a variety of randomized iterative algorithms for consistent linear systems. The framework includes the randomized Kaczmarz method that exponentially converges in the mean square whenever the system is consistent. For noisy linear systems corresponding to inconsistent systems, the randomized Kaczmarz method computes an approximate solution within a fixed distance depending on the norm of the noise vector. We extend this error analysi...



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In 2015, Gower and Richtárik presented a unifying framework for a variety of randomized iterative algorithms for consistent linear systems. The framework includes the randomized Kaczmarz method that exponentially converges in the mean square whenever the system is consistent. For noisy linear systems corresponding to inconsistent systems, the randomized Kaczmarz method computes an approximate solution within a fixed distance depending on the norm of the noise vector. We extend this error analysis to a general framework in inconsistent systems in a similar manner to Gower and Richtárik, and verify this theoretical analysis in numerical experiments.
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Created on
September 29
2018
bnewbold
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