Perturbation theory for the generalized Bott-Duffin inverse and its applications

摘要

A perturbation theory for the Bott-Duffin inverse A((L))((+)) of A with respect to a sub space L is developed. The perturbation bound for the solution of the constrained system Ax + y = b, x is an element of L, y is an element of L-perpendicular to is established, where A is an element of M-n(C), a subspace L subset of C-n and b is an element of C-n. Meanwhile this paper shows the generalized Bott-Duffin condition number K-gBD(A) = parallel toAparallel to.parallel toA((L))((+))parallel to to be inininium in the inequality of error analysis. (C) 2002 Elsevier Science Inc. All rights reserved. [References: 10]