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20 lines
1.2 KiB
Plaintext
20 lines
1.2 KiB
Plaintext
KKTDirect implements an ordering method and accompanying factorization for
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the direct solution of saddle-point matrices (also known as KKT or equilibrium
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matrices). A simple constraint on ordering together with an assumption on
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the rank of parts of the matrix are sufficient to guarantee the existence of
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the LDL^T factorization, stability concerns aside. In fact, D may be taken
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to be a diagonal matrix with +/-1 along the diagonal, and be fully determined
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prior to factorization, giving rise to a "signed Cholesky" factorization. A
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modified minimum-degree-like algorithm which incorporates this constraint is
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used, along with a simple algorithm to modify an existing fill-reducing
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ordering to respect the constraint. While a stability analysis is lacking,
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numerical experiments indicate that this is generally sufficient to avoid the
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need for numerical pivoting during factorization, with clear possible benefits
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for performance.
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Note this is only alpha-quality proof-of-concept code: for example,
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out-of-memory errors are not handled gracefully, and the provided Minimum
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Degree routine is not yet competitive with other packages.
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WWW: http://www.cs.ubc.ca/~rbridson/kktdirect/
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