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• W1979505770 abstract "In this paper, we present a simple combinatorial algorithm that solves symmetric diagonally dominant (SDD) linear systems in nearly-linear time. It uses little of the machinery that previously appeared to be necessary for a such an algorithm. It does not require recursive preconditioning, spectral sparsification, or even the Chebyshev Method or Conjugate Gradient. After constructing a nice spanning tree of a graph associated with the linear system, the entire algorithm consists of the repeated application of a simple update rule, which it implements using a lightweight data structure. The algorithm is numerically stable and can be implemented without the increased bit-precision required by previous solvers. As such, the algorithm has the fastest known running time under the standard unit-cost RAM model. We hope the simplicity of the algorithm and the insights yielded by its analysis will be useful in both theory and practice." @default.
• W1979505770 created "2016-06-24" @default.
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• W1979505770 date "2013-06-01" @default.
• W1979505770 modified "2023-09-23" @default.
• W1979505770 title "A simple, combinatorial algorithm for solving SDD systems in nearly-linear time" @default.
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• W1979505770 doi "https://doi.org/10.1145/2488608.2488724" @default.
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