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Randomized methods for linear constraints: convergence rates and conditioning

By D. Leventhal and A. S. Lewis


iterated projections, averaged projections, distance to ill-posedness, metric regularity AMS 2000 Subject Classification: 15A12, 15A39, 65F10, 90C25 We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of Strohmer and Vershynin for systems of linear equations, we show that, under appropriate probability distributions, the linear rates of convergence (in expectation) can be bounded in terms of natural linear-algebraic condition numbers for the problems. We relate these condition measures to distances to illposedness, and discuss generalizations to convex systems under metric regularity assumptions.

Topics: Key words, coordinate descent, linear constraint, condition number, randomization, error bound
Year: 2013
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