Condition number of Bott-Duffin inverse and their condition numbers

Further Results on Generalized Bott–duffin Inverses

Let A be a bounded linear operator, PM be an orthogonal projection with range M and PM ,N be an idempotent with range M and kernel N . This paper presents some novel relations between Bott-Duffin inverse AM = PM (APM + PM⊥) + and generalized Bott-Duffin inverse AM ,N = PM ,N (APM ,N + PN ,M ) + . Furthermore, the representations for the BottDuffin inverse and generalized Bott-Duffin inverse are...

Further results on generalized inverses in rings with involution

Let R be a unital ring with an involution. Necessary and sufficient conditions for the existence of the Bott-Duffin inverse of a ∈ R relative to a pair of self-adjoint idempotents (e, f) are derived. The existence of a {1, 3}-inverse, {1, 4}-inverse, and the Moore-Penrose inverse of a matrix product is characterized, and explicit formulas for their computations are obtained. Some applications t...

The Morse–Bott–Kirwan condition is local

On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems

Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and, in particular, a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this paper, we give explicit expressi...

Classical Network Synthesis Revisited

The talk consists of four parts. In the first part, the motivation is explained for revisiting certain questions in circuit theory, in particular, the synthesis theory of “one-port” (i.e. with a pair of external driving terminals) RLC networks and the questions of minimality associated with the Bott-Duffin procedure. The motivation relates to the synthesis of passive mechanical impedances and t...