Approaching Optimality for Solving SDD Linear Systems

0 Approaching optimality for solving SDD linear systems ∗

We present an algorithm that on input a graph G with n vertices and m+ n− 1 edges and a value k, produces an incremental sparsifier Ĝ with n − 1 +m/k edges, such that the condition number of G with Ĝ is bounded above by Õ(k log n), with probability 1− p. The algorithm runs in time Õ((m log n+ n log n) log(1/p)). As a result, we obtain an algorithm that on input an n × n symmetric diagonally dom...

Approaching optimality for solving SDD systems

We present an algorithm that on input of an n-vertex m-edge weighted graph G and a value k, produces an incremental sparsifier Ĝ with n− 1+m/k edges, such that the condition number of G with Ĝ is bounded above by Õ(k log n), with probability 1− p. The algorithm runs in time Õ((m logn+ n log n) log(1/p)). As a result, we obtain an algorithm that on input of an n × n symmetric diagonally dominant...

A ug 2 01 0 Approaching optimality for solving SDD linear systems ∗

We present an algorithm that on input of an n-vertex m-edge weighted graph G and a value k, produces an incremental sparsifier Ĝ with n− 1+m/k edges, such that the condition number of G with Ĝ is bounded above by Õ(k log n), with probability 1− p. The algorithm runs in time Õ((m logn+ n log n) log(1/p)). As a result, we obtain an algorithm that on input of an n × n symmetric diagonally dominant...

A METHOD FOR SOLVING FUZZY LINEAR SYSTEMS

In this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. Also necessary and sufficient conditions for existenceof solution are given. Some numerical examples illustrate the efficiencyof the method.

Defuzzification method for solving fuzzy linear systems