Finding effective support-tree preconditioners

In 1995, Gremban, Miller, and Zagha introduced supporttree preconditioners and a parallel algorithm called supporttree conjugate gradient (STCG) for solving linear systems of the form Ax = b, where A is an n × n Laplacian matrix. A Laplacian is a symmetric matrix in which the off-diagonal entries are non-positive, and the row and column sums are zero. A Laplacian A with 2m off-diagonal non-zeros can be interpreted as an undirected positively-weighted graph G with n vertices and m edges, where there is an edge between two vertices i and j with weight c((i, j)) = −Ai,j = −Aj,i if Ai,j = Aj,i < 0. Gremban et al. showed experimentally that STCG performs well on several classes of graphs commonly used in scientific computations. In his thesis, Gremban also proved upper bounds on the number of iterations required for STCG to converge for certain classes of graphs. In this paper, we present an algorithm for finding a preconditioner for an arbitrary graph G = (V, E) with n vertice...

• Type: Conference
• Year: 2005
• Where: SPAA
• Authors: Bruce M. Maggs, Gary L. Miller, Ojas Parekh, R. Ravi, Shan Leung Maverick Woo
• Keywords: Algorithm Called Supporttree, Distributed And Parallel Computing, Laplacian, Laplacian Matrix, SPAA 2005