# Solving for a Single Component of the Solution to a Linear System, Asynchronously

@inproceedings{Lee2014SolvingFA, title={Solving for a Single Component of the Solution to a Linear System, Asynchronously}, author={Christina E. Lee and Asuman E. Ozdaglar and Devavrat Shah}, year={2014} }

We present synchronous and asynchronous randomized variants of an algorithm for approximating a single component of the solution to a system of linear equations Ax = b, where A is a positive definite real matrix and b ∈ R. This can equivalently be formulated as solving for xi in x = Gx+ z for some G and z such that the spectral radius of G is less than 1. We consider the setting where n is large, yet G is sparse, i.e., each row has at most d nonzero entries. Our algorithm relies on the Neumann…

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