Recognition and ordering algorithms concerning global inheritance in LU factorisations

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dc.contributor.authorSlater, Terence Arthuren_US
dc.date.accessioned2024-08-15T18:23:24Z
dc.date.available2024-08-15T18:23:24Z
dc.date.copyright1988en_US
dc.date.issued1988
dc.degree.departmentDepartment of Computer Science
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractThe concept of forward lower restricted orderings of digraphs arises naturally from the study of inherited entries in LU factorizations of matrices. If a matrix A has a unique left unit LU factorization A = W then an entry u, 1 of U with J ~ i is said to be inher­ited from A if u, 1 = a, 1 for reasons related to the combinational structure of A and not because of the specific values of the nonzero matrix elements It can be proved that the entire strict upper triangular part of A is inherited if and only if the digraph D of the matrix has the property that for all, and J with, < J there is no path of length greater than one from , to J in D such that all intermediate nodes of the path are m { 1 2 , -1} Any digraph on the node set { 1 2 n } having this property is said to be forward lower restricted (FLR) ordered. We state and prove theorems which characterize the FLR ordered trees and the maxi­mal FLR ordered digraphs Polynomial time algorithms for deciding if a given ordered digraph is FLR ordered and for finding an FLR ordering of an arbitrary digraph are presented The latter algorithm also detects that a digraph is not FLR orderable In addi­tion, a more efficient algorithm for finding FLR orderings of digraphs containing a spanning tree is given some results concerning an attempt to characterize FLR orderable digraphs in terms of their cycle structure are included. All of the results of this thesis also extend to inheritance of entries in the matrix L of the LU factorization and to inheritance in UL factorizations.
dc.format.extent119 pages
dc.identifier.urihttps://hdl.handle.net/1828/19719
dc.rightsAvailable to the World Wide Weben_US
dc.titleRecognition and ordering algorithms concerning global inheritance in LU factorisationsen_US
dc.typeThesisen_US

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