Uniform approximation with radical functions
- Autores: Eduardo Corbacho Cortés
- Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Nº. 58, 2012, págs. 97-122
- Idioma: inglés
- DOI: 10.1007/bf03322606
- Enlaces
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Resumen
In this work we give a family of radical functions, ., uniformly dense in C [a, b]. This family does not satisfy the usual theorems of Approximation Theory about C [a, b]. The mathematical expression of the sequence that converges uniformly to every f 2 C [a, b] is determined. We present algorithms to approximate f with the uniform norm in different practical instances. A linear subspace of radical functions that verifies the Haar condition is constructed. We also study the degree of uniform approximation by radical functions and we show a comparative analysis with the approximation by arbitrary polynomials and Bernstein polynomials.
Until now the polynomials, the trigonometric functions and the rational functions have been the most used in Approximation Theory, but from now on it is possible that the radical functions can be employed too.
With this personal and original work, the reader is encouraged to come into the exciting world of the radical functions.
