Remarks on interpolation in certain linear spaces (III)
In this paper we study a way of extending the model of interpolating the real functions, with simple nodes, to the case of the functions defined between linear spaces, especially between linear normed spaces. In order to keep as many characteristics as possible from the case of the interpolation of...
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| Vydáno v: | Journal of numerical analysis and approximation theory Ročník 35; číslo 1 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Publishing House of the Romanian Academy
01.02.2006
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| Témata: | |
| ISSN: | 2457-6794, 2501-059X |
| On-line přístup: | Získat plný text |
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| Shrnutí: | In this paper we study a way of extending the model of interpolating the real functions, with simple nodes, to the case of the functions defined between linear spaces, especially between linear normed spaces. In order to keep as many characteristics as possible from the case of the interpolation of real functions, in this paper we present a model of construction of the abstract interpolation polynomials, based on the properties of multilinear mappings. In this case we will define the divided differences and establish interpolation formulas with the rest expressed as a divided difference. We give the example of the type of interpolation polynomial built for non-linear mappings between spaces of functions defined on a certain interval. |
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| ISSN: | 2457-6794 2501-059X |
| DOI: | 10.33993/jnaat351-1009 |