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 subspace L is developed. The perturbation bound for the solution of the constrained system Ax+y=b,x∈L,y∈L⊥ is established, where A∈Mn(C), a subspace L⊂Cn and b∈Cn. Meanwhile this paper shows the generalized Bott–Duffin condition number KgBD(A)=∥A∥·∥A(L)(+)∥ to be minimum in the inequality of error analysis.