A compact row storage scheme for Cholesky factors using elimination trees
ACM Transactions on Mathematical Software (TOMS)
On the storage requirement in the out-of-core multifrontal method for sparse factorization
ACM Transactions on Mathematical Software (TOMS)
Direct methods for sparse matrices
Direct methods for sparse matrices
A note on sparse factorization in a paging environment
SIAM Journal on Scientific and Statistical Computing
Equivalent sparse matrix reordering by elimination tree rotations
SIAM Journal on Scientific and Statistical Computing
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
A New Implementation of Sparse Gaussian Elimination
ACM Transactions on Mathematical Software (TOMS)
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
On the efficient solution of sparse systems of linear and nonlinear equations.
On the efficient solution of sparse systems of linear and nonlinear equations.
ACM SIGNUM Newsletter
Parallel and Fully Recursive Multifrontal Supernodal Sparse Cholesky
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Parallel and fully recursive multifrontal sparse Cholesky
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Adaptive paging for a multifrontal solver
Proceedings of the 18th annual international conference on Supercomputing
Reducing the I/O volume in an out-of-core sparse multifrontal solver
HiPC'07 Proceedings of the 14th international conference on High performance computing
Reducing the I/O Volume in Sparse Out-of-core Multifrontal Methods
SIAM Journal on Scientific Computing
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
ACM Transactions on Mathematical Software (TOMS)
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In this paper, we show that the multifrontal method can have significant advantage over the conventional sparse column-Cholesky scheme on a paged virtual memory system. A more than tenfold reduction in paging activities can be achieved, which saves as much as 20 percent in factorization time. We also introduce a hybrid sparse factorization method, which uses a mixture of column-Cholesky and submatrix-Cholesky operations. By switching to the use of frontal matrices from column-Cholesky operations at appropriate columns, we demonstrate that the proposed hybrid scheme has an advantage over the sparse column-Cholesky method in reducing paging activities and over the multifrontal method in its adaptability to the amount of available working storage.