Data structures and network algorithms
Data structures and network algorithms
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
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
A graph partitioning algorithm by node separators
ACM Transactions on Mathematical Software (TOMS)
The influence of relaxed supernode partitions on the multifrontal method
ACM Transactions on Mathematical Software (TOMS)
The multifrontal method and paging in sparse Cholesky factorization
ACM Transactions on Mathematical Software (TOMS)
A generalized envelope method for sparse factorization by rows
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Improving Parallel Ordering of Sparse Matrices Using Genetic Algorithms
Applied Intelligence
Algorithm 849: A concise sparse Cholesky factorization package
ACM Transactions on Mathematical Software (TOMS)
Dynamic Supernodes in Sparse Cholesky Update/Downdate and Triangular Solves
ACM Transactions on Mathematical Software (TOMS)
Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning
SIAM Journal on Scientific Computing
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For a given sparse symmetric positive definite matrix, a compact row-oriented storage scheme for its Cholesky factor is introduced. The scheme is based on the structure of an elimination tree defined for the given matrix. This new storage scheme has the distinct advantage of having the amount of overhead storage required for indexing always bounded by the number of nonzeros in the original matrix. The structural representation may be viewed as storing the minimal structure of the given matrix that will preserve the symbolic Cholesky factor. Experimental results on practical problems indicate that the amount of savings in overhead storage can be substantial when compared with Sherman's compressed column storage scheme.