The Gasca–Maeztu conjecture for $$n=5$$ n = 5
| العنوان: | The Gasca–Maeztu conjecture for $$n=5$$ n = 5 |
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| المؤلفون: | Georg Zimmermann, Hakop Hakopian, Kurt Jetter |
| المصدر: | Numerische Mathematik. 127:685-713 |
| بيانات النشر: | Springer Science and Business Media LLC, 2013. |
| سنة النشر: | 2013 |
| مصطلحات موضوعية: | Set (abstract data type), Combinatorics, Computational Mathematics, Conjecture, Total degree, Applied Mathematics, Numerical analysis, Bivariate interpolation, Mathematics |
| الوصف: | An $$n$$ n -poised set in two dimensions is a set of nodes admitting unique bivariate interpolation with polynomials of total degree at most $$n$$ n . We are interested in poised sets with the property that all fundamental polynomials are products of linear factors. Gasca and Maeztu (Numer Math 39:1---14, 1982) conjectured that every such set necessarily contains $$n+1$$ n + 1 collinear nodes. Up to now, this had been confirmed only for $$n\le 4$$ n ≤ 4 , the case $$n=4$$ n = 4 having been proved for the first time by Busch (Rev Un Mat Argent 36:33---38, 1990). In the present paper, we prove the case $$n=5$$ n = 5 with new methods that might also be useful in deciding the still open cases for $$n\ge 6$$ n ? 6 . |
| تدمد: | 0945-3245 0029-599X |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_________::f4d44ba38b9b8197310ccc67b9b7c0cbTest https://doi.org/10.1007/s00211-013-0599-4Test |
| حقوق: | CLOSED |
| رقم الانضمام: | edsair.doi...........f4d44ba38b9b8197310ccc67b9b7c0cb |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 09453245 0029599X |
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