Non-polynomial divided difference and blossoming
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910055005159424 |
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| author | Zürnacı-Yetiş, Fatma |
| author_facet | Zürnacı-Yetiş, Fatma |
| contents | Two notable examples of dual functionals in approximation theory and computer-aided geometric design are the blossom and the divided difference operator. Both of these dual functionals satisfy a similar set of formulas and identities. Moreover, the divided differences of polynomials can be expressed in terms of the blossom. In this paper, an extended non-polynomial homogeneous blossom for a wide collection of spline spaces, including trigonometric splines, hyperbolic splines, and special Müntz spaces of splines, is defined. It is shown that there is a relation between the non-polynomial divided difference and the blossom, which is analogous to the polynomial case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_21891 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-polynomial divided difference and blossoming Zürnacı-Yetiş, Fatma Numerical Analysis 65D17, 41A10 Two notable examples of dual functionals in approximation theory and computer-aided geometric design are the blossom and the divided difference operator. Both of these dual functionals satisfy a similar set of formulas and identities. Moreover, the divided differences of polynomials can be expressed in terms of the blossom. In this paper, an extended non-polynomial homogeneous blossom for a wide collection of spline spaces, including trigonometric splines, hyperbolic splines, and special Müntz spaces of splines, is defined. It is shown that there is a relation between the non-polynomial divided difference and the blossom, which is analogous to the polynomial case. |
| title | Non-polynomial divided difference and blossoming |
| topic | Numerical Analysis 65D17, 41A10 |
| url | https://arxiv.org/abs/2512.21891 |