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- W4300100552 abstract "In this paper, we present a simple combinatorial algorithm that solves symmetric diagonally dominant (SDD) linear systems in nearly-linear time. It uses very 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 (non-recursive) 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 that the simplicity of the algorithm and the insights yielded by its analysis will be useful in both theory and practice." @default.
- W4300100552 created "2022-10-03" @default.
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- W4300100552 date "2013-01-28" @default.
- W4300100552 modified "2023-09-25" @default.
- W4300100552 title "A Simple, Combinatorial Algorithm for Solving SDD Systems in Nearly-Linear Time" @default.
- W4300100552 doi "https://doi.org/10.48550/arxiv.1301.6628" @default.
- W4300100552 hasPublicationYear "2013" @default.
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