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Approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions

โœ Scribed by A.N. Gorban

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
315 KB
Volume
11
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

Linear spaces of continuous functions of real variables closed under the superposition operation are considered. It has been proved that when such a space contains constants, linear functions, and at least one nonlinear function, it is dense in the space of all continuous functions in the topology of uniform convergence on compact sets.

So, the approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions is possible.

๐Ÿ“œ SIMILAR VOLUMES

Approximation of continuous functions on
Approximation of continuous functions on Rd by linear combinations of shifted rotations of a sigmoid function with and without scaling
โœ Yoshifusa Ito ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 909 KB

Abslracl--Let f be an arbitrary continuous function defined on R d and h be any sigmoid function. Then, there is a linear combination of scaled shifted rotations of h, which approximates f uniformly on the whole space R d, if a certain such linear combination approximates f uniformly in a neighbourh