Some Schur complement identities and applications to matrix extrapolation methods

SOLVING FUZZY LINEAR SYSTEMS BY USING THE SCHUR COMPLEMENT WHEN COEFFICIENT MATRIX IS AN M-MATRIX

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...

Applications of Dual Schur Complement

Some new identities for Schur functions

Some new identities for Schur functions are proved. In particular, we settle in the affirmative a recent conjecture of Ishikawa-Wakayama [5] and solve a problem raised by Bressoud [2].

A preconditioner for the Schur complement matrix

A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a problem in a narrow strip around the interface. It requires much less memory and computing time than classical Neumann-Neumann preconditioner and its variants, and handles correctly the flux splitting among subdomains that shar...

Periodic Schur Form and Some Matrix Equations

We propose an elegant and conceptually simple method for computing the periodic solution of three classes of periodic matrix equations | Ric-cati, Lyapunov and Sylvester. Such equations arise naturally in several problems of linear system theory. Our approach is very attractive from a numerical point of view, since it is based on the periodic Schur form of techniques involving unitary (orthogon...