Sparse Cholesky factorization on a multiprocessor
Systems of linear equations of the form Ax = b, where A is a large sparse symmetric positive definite matrix, arise frequently in science and engineering. The sequential computation of the solution vector x is well understood and may algorithms for this problem employ the following steps. First, try to reorder the rows and columns of A so that its Cholesky factor L is sparse. Next, determine the structure of L by symbolically factoring A and allocate storage for L. Finally, numerically factor A and then compute x by solving the triangular systems Ly = b and L/sup T/ x = y. This thesis presents parallel algorithms for the different steps of this computation. The algorithms are designed for message-passing multiprocessors. The algorithms limit communication overhead and can solve problems that are too large to reside in the memory of any single processor. Numerical results based upon an implementation on an Intel hypercube are presented.
- Research Organization:
- Cornell Univ., Ithaca, NY (USA)
- OSTI ID:
- 7183866
- Country of Publication:
- United States
- Language:
- English
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