Treffer: Condition number of Bott–Duffin inverse and their condition numbers: Condition number of Bott-Duffin inverse and their condition numbers

The paper studies the normwise relative condition number of the Bott-Duffin inverse and the corresponding condition number for the constrained linear systems \(Ax+y=b,x\in L,y\in L^{\bot }\). Since the condition number cannot be computed exactly, the authors consider the sensitivity of the problem ``the condition number of the condition number'' by introducing and study the bounds of the level-2 condition number for the Bott-Duffin inverse and the constrained linear system. Finally, the paper reviews results on componentwise condition number and derives upper bound on their sensitivity. When the matrix is nonsingular the results of the paper cover the results of \textit{D. J. Highman} [Linear Algebra Appl. 214, 193-213 (1995; Zbl 0816.15004)].