The Fan-Both Family of Column-Based Distributed Cholesky Factorization Algorithms

There are two classic column-based Cholesky factorization methods, the fan-out method that communicates factor columns among processors, and the fan-in method that communicates aggregate update columns among processors. In this paper we show that these two very different methods are members of a “fan-both” algorithm family.

[1]  Cleve Ashcraft,et al.  A Fan-In Algorithm for Distributed Sparse Numerical Factorization , 1990, SIAM J. Sci. Comput..

[2]  Joseph W. H. Liu,et al.  Modification of the minimum-degree algorithm by multiple elimination , 1985, TOMS.

[3]  Robert Francis Lucas.  Solving planar systems of equations on distributed-memory multiprocessors , 1988 .

[4]  Laurie A. Hulbert,et al.  Limiting Communication in Parallel Sparse Cholesky Factorization , 1991, SIAM J. Sci. Comput..

[5]  A. George.  Nested Dissection of a Regular Finite Element Mesh , 1973 .

[6]  Joseph W. H. Liu,et al.  Computational models and task scheduling for parallel sparse Cholesky factorization , 1986, Parallel Comput..

[7]  Robert Schreiber,et al.  A New Implementation of Sparse Gaussian Elimination , 1982, TOMS.

[8]  Joseph W. H. Liu.  The role of elimination trees in sparse factorization , 1990 .

[9]  Joseph W. H. Liu,et al.  A Comparison of Three Column-Based Distributed Sparse Factorization Schemes. , 1990 .

[10]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[11]  J. G. Lewis,et al.  A fast algorithm for reordering sparse matrices for parallel factorization , 1989 .

[12]  Alan George,et al.  Communication results for parallel sparse Cholesky factorization on a hypercube , 1989, Parallel Comput..

[13]  John G. Lewis,et al.  Sparse matrix test problems , 1982, SGNM.

[14]  Michael T. Heath,et al.  Sparse Cholesky factorization on a local-memory multiprocessor , 1988 .