Preconditioning Methods for Linear Systems with Saddle Point Matrices

摘要

Preconditioning methods for matrices on saddle point form, as typically arising in constrained optimization problems, are surveyed. Special consideration is given to two methods: a nearly symmetric block incomplete factorization preconditioning method and an indefinite matrix preconditioner. Both methods result in eigenvalues with positive real parts and small or zero imaginary parts. The behaviour of the methods are illustrated on solving a regularized Stokes problem. ...