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• W2102560346 abstract "We present an improved algorithm for solving symmetrically diagonally dominant linear systems. On input of an n×n symmetric diagonally dominant matrix A with m non-zero entries and a vector b such that Ax̅ = b for some (unknown) vector x̅, our algorithm computes a vector x such that ∥x-x̅∥ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>A</sub> ≤ϵ∥x̅∥ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>A</sub> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sup> in time Õ (m log n log (1/ϵ)) <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sup> . The solver utilizes in a standard way a 'preconditioning' chain of progressively sparser graphs. To claim the faster running time we make a two-fold improvement in the algorithm for constructing the chain. The new chain exploits previously unknown properties of the graph sparsification algorithm given in [Koutis,Miller,Peng, FOCS 2010], allowing for stronger preconditioning properties.We also present an algorithm of independent interest that constructs nearly-tight low-stretch spanning trees in time Õ (m log n), a factor of O (log n) faster than the algorithm in [Abraham,Bartal,Neiman, FOCS 2008]. This speedup directly reflects on the construction time of the preconditioning chain." @default.
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• W2102560346 date "2011-10-01" @default.
• W2102560346 modified "2023-10-18" @default.
• W2102560346 title "A Nearly-m log n Time Solver for SDD Linear Systems" @default.
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• W2102560346 doi "https://doi.org/10.1109/focs.2011.85" @default.
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