Nearly Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems

SIAM Journal on Matrix Analysis and Applications, Volume 35, Issue 3, 2014, Pages 835-885.

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Keywords:
numerical analysislinear systemdata structurerandomized algorithm

Abstract:

We present a randomized algorithm that, on input a symmetric, weakly diagonally dom- inant n-by-n matrix A with m non-zero entries and an n-vector b, produces anx such that k x − ˜ x k A ≤ ǫ k x k A, where Ax = b, in expected time

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