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- W1557739832 abstract "In systems and control it is important to know under what conditions a class of algorithms is linear, since linearity is a key property for problems requiring fast computations. In this paper we prove that for the purpose of function estimation, and more generally of approximation in normed spaces, a Hilbert structure for the class of functions being approximated is necessary as well as sufficient for linearity of the following classes of approximation algorithms: spline, interpolatory, strongly optimal, and almost strongly optimal. This provides a converse to the well-known result that a Hilbert structure is sufficient for such linearity properties." @default.
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- W1557739832 date "1992-06-01" @default.
- W1557739832 modified "2023-09-23" @default.
- W1557739832 title "A Characterization of Spaces Admitting Linear Algorithms" @default.
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- W1557739832 doi "https://doi.org/10.23919/acc.1992.4792071" @default.
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