A Nearly-Linear Time Algorithm for Approximately Solving Linear Systems in a Symmetric M-Matrix
نویسندگان
چکیده
We present an algorithm for solving a linear system in a symmetric M-matrix. In particular, for n × n symmetric M-matrix M , we show how to find a diagonal matrix D such that DMD is diagonallydominant. To compute D, the algorithm must solve O (log n) linear systems in diagonally-dominant matrices. If we solve these diagonallydominant systems approximately using the Spielman-Teng nearly-linear time solver [1], then we obtain an algorithm for approximately solving linear systems in symmetric M-matrices, for which the expected running time is also nearly-linear.
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