Solving Sparse Linear Systems Faster than Matrix Multiplication

  title={Solving Sparse Linear Systems Faster than Matrix Multiplication},
  author={Richard Peng and Santosh S. Vempala},
Can linear systems be solved faster than matrix multiplication? While there has been remarkable progress for the special cases of graph structured linear systems, in the general setting, the bit complexity of solving an $n \times n$ linear system $Ax=b$ is $\tilde{O}(n^\omega)$, where $\omega < 2.372864$ is the matrix multiplication exponent. Improving on this has been an open problem even for sparse linear systems with poly$(n)$ condition number. In this paper, we present an algorithm that… 

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