Inners and Schur complement

On Preconditioning Schur Complement and Schur Complement Preconditioning

We study two implementation strategies to utilize Schur complement technique in multilevel recursive incomplete LU preconditioning techniques (RILUM) for solving general sparse matrices. The first strategy constructs a RILUM to precondition the original matrix. The second strategy solves the first Schur complement matrix using the lower level parts of the RILUM as the preconditioner. We discuss...

Applications of Dual Schur Complement

On Inertia and Schur Complement in Optimization

Partitioned symmetric matrices, in particular the Hessian of the Lagrangian, play a fundamental role in nonlinear optimization. For this type of matrices S.-P. Han and 0. Fujiwara recently presented an inertia theorem under a certain regularity assumption. We prove that this theorem is true without any regularity assumption. Then we consider matrix extensions preserving the sign of the determin...

Additive Schwarz for the Schur Complement Method Additive Schwarz for the Schur Complement Method

Submitted to the proceedings of the ninth international conference on domain decomposition methods (Bergen-Norway-1996).

Block Diagonal Preconditioners for the Schur Complement Method Block Diagonal Preconditioners for the Schur Complement Method

We present numerical methods for solving systems of linear equations originated from the discretisation of two-dimensional elliptic partial diierential equations. We are interested in diierential equations that describe heterogeneous and anisotropic phenomena. We use a nonoverlapping domain decomposition method for solving the linear systems. We describe new local preconditioners for the interf...