Operators on anti-dual pairs: Generalized Schur complement

Applications of Dual Schur Complement

A Generalized Schur Complement for Non-negative Operators on Linear Spaces

Extending the corresponding notion for matrices or bounded linear operators on a Hilbert space we define a generalized Schur complement for a non-negative linear operator mapping a linear space into its dual and derive some of its properties.

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...

Representations of generalized inverses of partitioned matrix involving Schur complement

In this article, we consider some representations of {1, 3}, {1, 4}, {1, 2, 3} and {1, 2, 4}-inverses of a partitioned matrix M which are equivalent to some rank additivity conditions. We present some applications of these results to generalizations of the Sherman-Morrison-Woodbury-type formulae.

Dual Schur Complement Method for Semi-Definite Problems

Semi-definite problems are encountered in a wide variety of engineering problems. Most domain decomposition methods efficient for parallel computing are based on iterative schemes and rarely address the problem of checking the problem’s singularity and computing the null space. In this paper we present a simple and efficient method for checking the singularity of an operator and for computing a...