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Solving sparse, symmetric, diagonally-dominant linear systems in time O(m1.31

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2 Author(s)
D. A. Spielman ; Dept. of Math., Massachusetts Inst. of Technol., Cambridge, MA, USA ; Shang-Hua Teng

We present a linear-system solver that, given an n-by-n symmetric positive semi-definite, diagonally dominant matrix A with m non-zero entries and an n-vector b, produces a vector x˜ within relative distance ε of the solution to Ax = b in time O(m1.31log(n/ε)bO(1)), where b is the log of the ratio of the largest to smallest non-zero entry of A. If the graph of A has genus m or does not have a K minor, then the exponent of m can be improved to the minimum of 1 + 5θ and (9/8)(1 + θ). The key contribution of our work is an extension of Vaidya's techniques for constructing and analyzing combinatorial preconditioners.

Published in:

Foundations of Computer Science, 2003. Proceedings. 44th Annual IEEE Symposium on

Date of Conference:

11-14 Oct. 2003