An Efficient Parallel Solver for SDD Linear Systems

Daniel A. Spielman; Richard Peng

An Efficient Parallel Solver for SDD Linear Systems

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arxiv 1311.3286 v1 pith:JTTHKZEU submitted 2013-11-13 cs.NA cs.DScs.NA

Richard Peng , Daniel A. Spielman This is my paper · ORCID

classification cs.NAcs.DS

keywords algorithmmatricessystemsequationsinverselinearparallelsolving

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We present the first parallel algorithm for solving systems of linear equations in symmetric, diagonally dominant (SDD) matrices that runs in polylogarithmic time and nearly-linear work. The heart of our algorithm is a construction of a sparse approximate inverse chain for the input matrix: a sequence of sparse matrices whose product approximates its inverse. Whereas other fast algorithms for solving systems of equations in SDD matrices exploit low-stretch spanning trees, our algorithm only requires spectral graph sparsifiers.

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