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Optimal inverses and abstract splines
(Elsevier Science Inc, 2016-05)
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 ...
Indefinite Abstract Splines with a Quadratic Constraint
(Springer/Plenum Publishers, 2020-06)
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 ...
Correction to: Indefinite Abstract Splines with a Quadratic Constraint
(Springer/Plenum Publishers, 2021-10)
In the statement of Lemma 4.1 is incorrect. In fact, if the dimension of H is infinite it is always possible to find a sequence in CV which converges weakly to a vector not contained in CV , see Proposition 2.1 below. We ...
Saddle point problems, Bott-Duffin inverses, abstract splines and oblique projections
(Elsevier, 2014-06)
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 ...
Refinable spaces and local approximation estimates for hierarchical splines
(Oxford University Press, 2017-07)
We study the local approximation properties in hierarchical spline spaces through multiscale quasi-interpolation operators. This construction suggests the analysis of a subspace of the classical hierarchical spline space ...