A generalization of the Bott–Duffin inverse and its applications

Abstract

AbstractThe ‘constrained inverse’ was introduced by Bott and Duffin in 1953. Since then various generalizations have arisen. In this paper, we propose a generalization of the Bott–Duffin inverse. Applications of the projection methods for solving sparse linear systems, the truncated methods for solving least squares problems, and solvers for generalized saddle point problems are also presented. The relationships with other generalized Bott–Duffin inverses are explored. The results indicate that the generalized Bott–Duffin inverse may be a useful tool in matrix computations. Copyright © 2008 John Wiley & Sons, Ltd.