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Randomized Kaczmarz solver for noisy linear systems. (English) Zbl 1195.65038
The method of S. Kaczmarz [Bull. Int. Acad. Polon. Sci. A 1937, 355–357 (1937; Zbl 0017.31703)] is an iterative algorithm for solving systems of linear equations \(A x = b\). It is proved that in the noisy version \(A x \approx b+r,\) where \(r\) is an arbitrary error vector, the randomized method reaches an error threshold dependent on the matrix \(A\) with the same rate as in the error-free case. Examples are shown that the authors results are sharp in the general context.

65F10 Iterative numerical methods for linear systems
60H25 Random operators and equations (aspects of stochastic analysis)
65C50 Other computational problems in probability (MSC2010)
Full Text: DOI arXiv
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