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Randomized Kaczmarz with Averaging

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arxiv 2002.04126 v1 pith:PW3EHYK4 submitted 2020-02-10 math.NA cs.NA

Randomized Kaczmarz with Averaging

Jacob D. Moorman , Thomas K. Tu , Denali Molitor , Deanna Needell This is my paper
classification math.NA cs.NA
keywords convergencemethodaveragingkaczmarzparallelrandomizedsystemsupdates
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The randomized Kaczmarz (RK) method is an iterative method for approximating the least-squares solution of large linear systems of equations. The standard RK method uses sequential updates, making parallel computation difficult. Here, we study a parallel version of RK where a weighted average of independent updates is used. We analyze the convergence of RK with averaging and demonstrate its performance empirically. We show that as the number of threads increases, the rate of convergence improves and the convergence horizon for inconsistent systems decreases.

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