Saddle point systems arise widely in optimization problems with constraints. The utility of Schur complement approximation is now broadly appreciated in the context of solving such saddle point systems by iteration. In this short manuscript, we present a new Schur complement approximation for PDE constrained optimization, an important class of these problems. Block diagonal and block triangular...

We consider several preconditioners for the pressure Schur complement of the discrete steady Oseen problem. Two of the preconditioners are well known from the literature and the other is new. Supplemented with an appropriate approximate solve for an auxiliary velocity subproblem these approaches give rise to a family of the block preconditioners for the matrix of the discrete Oseen system. In t...

Abstract. Several Schur complement-based preconditioners have been proposed for solving (generalized) saddle-point problems. We consider matrices where the Schur complement has rapid decay over some graph known a priori. This occurs for many matrices arising from the discretization of systems of partial differential equations, and this graph is then related to the mesh. We propose the use of pr...

In the nonoverlapping approach to domain decomposition (cf. [10], [21] and the references therein) the nite element equation for an elliptic boundary value problem is reduced, after parallel subdomain solves, to its Schur complement which involves only the nodal variables (degrees of freedom) on the subdomain boundaries. The condition number of the Schur complement has been investigated for sec...

ing this paper new factorization techniques for computation of the Operational Space Mass Matrix (A) and its inverse (A-l) are developed. Starting with a new factorization of the inverse of mass matrix (M-l) in the form of Schur Complement as M-l = G’ %)TsI-lB, where d and 8 are block tridlagonal matrices and G is a tridiagonal matrix, similar factorization for A and A-i are derived. Specifical...

This paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp M-matrix. Thefuzzy linear system (FLS) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. However, solving this crisp system isdifficult for large n because of dimensionality problems . It is shown that thisdifficulty may be avoide...