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Otherwise, SCPRE permutes the blocks and builds a block upper-triangular preconditioner.
If we symmetrically permute B with the permutation matrix [[[e.
1981) showed how the barycenter heuristic can be used as a subalgorithm of a larger algorithm to permute the vertices in the hierarchical layers so that the number of crossings is minimized.
Whenever a move labeling an edge e of a James-Peel tree just permutes rows or columns, we can eliminate that move from the tree at the cost of relabeling rows and columns of James-Peel moves below e.
Once we know how to permute one large block that contains at least two subblocks into two blocks, we can employ this procedure recursively.
This formula takes no account of the word length or the freedom to permute the letters, let alone the fact that the number of permutations depends on the letter-pattern of the words.
a matching in which every row vertex is matched) can be used to permute columns (or rows) A to bring nonzeros to the diagonal.
It is interesting to note that some capital placenames exist in the UK, and others permute into other placenames in North America.
If we renumber the in-tree arcs first and the out-of-tree arcs last, we can permute the in-tree arcs and the nodes such that the permuted matrix A has the form
By symmetrically renumbering the rows and columns of the coefficient matrix using a tree-based postordering, we can permute the matrix into a bordered block triangular form while preserving the elimination tree.
n-1] is just a transposition, and thus cannot permute more than two elements of [n] at a time.