Preconditioning Reduced Matrices

We study preconditioning strategies for linear systems with positive-deenite matrices of the form Z T GZ, where Z is rectangular and G is symmetric but not necessarily positive deenite. The preconditioning strategies are designed to be used in the context of a conjugate-gradient iteration, and are suitable within algorithms for constrained optimization problems. The techniques have other uses, however, and are applied here to a class of problems in the calculus of variations. Numerical tests are also included.