We extend the notion of optimal inverse introduced by S.K. Mitra for matrices, to operators in Hilbert spaces. We obtain necessary and sufficient conditions for the existence of these inverses for a closed range operator ...

In this note, we present links between several different areas in numerical analysis and operator theory. More precisely, we show that several saddle point problems are solvable in the presence of a property (called ...

We study an extension to Krein spaces of the abstract interpolating spline problem in Hilbert spaces, introduced by M. Atteia. This is a quadratically constrained quadratic programming problem, where the objective function ...

We study three well-known minimization problems in Hilbert spaces: the weighted least squares problem and the related problems of abstract splines and smoothing. In each case we analyze the solvability of the problem for ...

A generalization with singular weights of Moore–Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators.

Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in ...