Optimization problems with constraints which require the solution of a partial differential equation arise widely in many areas of the sciences and engineering, in particular in problems of design.â€¦ (More)

We consider the application of the conjugate gradient method to the solution of large, symmetric indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a newâ€¦ (More)

We consider the application of the conjugate gradient method to the solution of large symmetric, indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a newâ€¦ (More)

We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle-point problems or, in particular, regularizations thereof. Such methodsâ€¦ (More)

We present a modified version of the approximate minimum degree algorithm for preordering a matrix with a symmetric sparsity pattern prior to the numerical factorization. The modification is designedâ€¦ (More)

Saddle-point systems arise in many applications areas, in fact in any situation where an extremum principle arises with constraints. The Stokes problem describing slow viscous flow of anâ€¦ (More)

Recently a number of variants of the approximate minimum degree algorithm have been proposed that aim to efficiently order symmetric matrices containing some dense rows. We compare the performance ofâ€¦ (More)

The problem of finding good preconditioners for the numerical solution of an important class of indefinite linear systems is considered. These systems are of a regularized saddle point structure [ Aâ€¦ (More)