Perturbation analysis for the generalized Schur complement of a positive semi‐definite matrix
Musheng Wei, Minghui Wang · Numerical Linear Algebra with Applications · 2007
Abstract Let and S = C − B H A † B be the generalized Schur complement of A ⩾0 in P . In this paper, some perturbation bounds of S are presented which generalize the result of Stewart ( Technical Report TR‐95‐38 , University of Maryland, 1995) and enrich the perturbation theory for the Schur complement. Also, an error estimate for the smallest perturbation of C , which lowers the rank of P , is discussed. Copyright © 2007 John Wiley & Sons, Ltd.