On linearity of spline algorithms
Mark Kon, R Tempoi · Journal of Complexity · 1989
In this paper we prove that a Hilbert structure is necessary as well as sufficient for linearity of the following classes of Banach space approximation algorithms: spline, interpolatory, strongly optimal, and almost strongly optimal. In the context of information-based complexity, this provides a converse to the well-known result that a Hilbert structure is sufficient for such linearity properties.