Nearly Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems
نویسندگان
چکیده
منابع مشابه
Nearly-Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems
We present a randomized algorithm that, on input a weakly diagonally dominant symmetric n-by-n matrix A with m non-zero entries and an n-vector b, produces an x̃ such that ‖x − x̃‖ A ≤ ǫ ‖x‖ A , where Ax = b, in expected time m log n log(1/ǫ). The algorithm applies subgraph preconditioners in a recursive fashion. These preconditioners improve upon the subgraph preconditioners first introduced by ...
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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 x̃ within relative distance ǫ of the solution to Ax = b in time O(m log(nκf (A)/ǫ)), where κf (A) is the log of the ratio of the largest to smallest non-zero eigenvalue of A. In particular, log(κf (A)) = O(b log n), wh...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2014
ISSN: 0895-4798,1095-7162
DOI: 10.1137/090771430