Birkhoff Polynomial Basis
| Autor: | Nikta Shayanfar, Amirhossein Amiraslani, Heike Faßbender |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Polynomial
010102 general mathematics MathematicsofComputing_NUMERICALANALYSIS Monomial basis Birkhoff interpolation 01 natural sciences Polynomial interpolation Matrix polynomial 010101 applied mathematics Polynomial basis Hermite interpolation ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Applied mathematics 0101 mathematics Interpolation Mathematics |
| Zdroj: | Springer Proceedings in Mathematics & Statistics ISBN: 9783319499826 |
| DOI: | 10.1007/978-3-319-49984-0_1 |
| Popis: | The Birkhoff interpolation problem is an extension of the well-known Lagrange and Hermite interpolation problems. We propose a new set of basis polynomials for representing the Birkhoff interpolation polynomial . The proposed basis extends the definition of the Newton basis for non-distinct interpolation nodes. This approach allows to determine the Birkhoff interpolation polynomial via a special linear system of equations. When applied to the special cases of Taylor, Lagrange and Hermite interpolations, this approach reduces to the well-known solutions of these problems expressed in the Newton basis . A number of examples are studied. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|