Sparse Cholesky Elimination Tree
5 hours ago
- #sparse Cholesky
- #elimination tree
- #factorization algorithm
- Derivation of elimination tree for sparse Cholesky factorization, focusing on right-looking algorithm and its role in determining fill-in and task dependencies.
- Transition from dense Cholesky algorithm to sparse case, highlighting how elimination tree predicts fill-in and column dependencies without performing dense factorization.
- Explanation of structural rule: if L[i][k] and L[j][k] are nonzero (k < j ≤ i), then L[i][j] must be nonzero, leading to redundant edges in task DAG that form a tree.
- Description of symbolic Cholesky function to compute nonzero pattern of L using elimination tree and original matrix sparsity.
- Algorithm to compute elimination tree from original sparse matrix pattern, using ancestor arrays to determine parent relationships without extra work.