Given a block symmetric matrix
where has rows and columns and has rows and columns, this package constructs preconditioners of the form
Here, the leading block matrix is a suitably chosen approximation to ; it may either be prescribed explicitly, in which case a symmetric indeﬁnite factorization of will be formed using HSL_MA57, or implicitly. In the latter case, will be ordered to the form
where is a permutation and is an invertible sub-block (“basis”) of the columns of ; the selection and factorization of uses HSL_MA48 — any dependent rows in are removed at this stage. Once the preconditioner has been constructed, solutions to the preconditioning system
may be computed.
Full advantage is taken of any zero coeﬃcients in the matrices , and .