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Full Record Details
DOI
10.5286/raltr.2009016
Persistent URL
http://purl.org/net/epubs/work/51037
Record Status
Checked
Record Id
51037
Title
Combinatorial problems in solving linear systems
Contributors
IS Duff (STFC Rutherford Appleton Lab.)
,
B Ucar
Abstract
Numerical linear algebra anhd combinational optomization are vast subjects; as is their interaction. In virtually all cases there should be a notion of sparsity for a combinatorial problem to arise. Sparse matrices therefore form the basis of the interaction of these seemingly disparate subjects. As the core of many of today's numerical linear algebra computations consists of the solution of sparse linear system by direct or iterative methods, we survey some cominatorial problems, ideas, and algorithms relating to these computations. On the direct methods side, we discuss issues such as matrix ordering; bipartite matching and matrix scaling for better pivoting; task assignment and scheduling for parallel multifrontal solvers. On the iterative side, we discuss the preconditioning techniques including incomplete factorization preconditioners, support graph preconditioners, and algebraic multigrid. In a seperate part, we discuss the block trianglar form of sparse matrices.
Organisation
CSE
,
CSE-NAG
,
STFC
Keywords
combinatorial optimization
,
Combinatotial scintifc computing
,
linear system solution
,
graph theory
,
sparse matrices
Funding Information
Related Research Object(s):
Licence Information:
Language
English (EN)
Type
Details
URI(s)
Local file(s)
Year
Report
RAL Technical Reports
RAL-TR-2009-016. STFC, 2009.
duucRAL2009016.pdf
2009
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