Version 1.2.0

10th April 2013

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HSL_MI13 Preconditioners for saddle-point systems

Given a block symmetric matrix

KH = H AT A C ,

where H has n rows and columns and A has m rows and n columns, this package constructs preconditioners of the form

KG = G AT A C .

Here, the leading block matrix G is a suitably chosen approximation to H; it may either be prescribed explicitly, in which case a symmetric indefinite factorization of KG will be formed using HSL_MA57, or implicitly. In the latter case, KG will be ordered to the form

KG = P G11G21TA1T G21 G22 A2T A1 A2 C PT

where P is a permutation and A1 is an invertible sub-block (“basis”) of the columns of A; the selection and factorization of A1 uses HSL_MA48 — any dependent rows in A are removed at this stage. Once the preconditioner has been constructed, solutions to the preconditioning system

G AT A C x y = ab

may be computed.

Full advantage is taken of any zero coefficients in the matrices H, A and C.