High relative accuracy for a Newton form of bivariate interpolation problems
The problem of bivariate polynomial interpolation using Newton-type bases is examined, leading to the application of a generalized Kronecker matrix product. Algorithms for computing the coefficients of the interpolating polynomial are presented, along with conditions that ensure relative errors of t...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025178 |
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| author | Yasmina Khiar Esmeralda Mainar Eduardo Royo-Amondarain Beatriz Rubio |
| author_facet | Yasmina Khiar Esmeralda Mainar Eduardo Royo-Amondarain Beatriz Rubio |
| author_sort | Yasmina Khiar |
| collection | DOAJ |
| description | The problem of bivariate polynomial interpolation using Newton-type bases is examined, leading to the application of a generalized Kronecker matrix product. Algorithms for computing the coefficients of the interpolating polynomial are presented, along with conditions that ensure relative errors of the order of machine precision. A generalization of the classical recursion formula of divided differences in two dimensions is proposed for grids that generalize the standard rectangular layout. Numerical experiments demonstrate the high accuracy achieved by the proposed approach. |
| format | Article |
| id | doaj-art-e5e530089b544efdbeef0704ebcadf48 |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-e5e530089b544efdbeef0704ebcadf482025-08-20T03:17:09ZengAIMS PressAIMS Mathematics2473-69882025-02-011023836384710.3934/math.2025178High relative accuracy for a Newton form of bivariate interpolation problemsYasmina Khiar0Esmeralda Mainar1Eduardo Royo-Amondarain2Beatriz Rubio3Departamento de Matemática Aplicada / IUMA, Universidad de Zaragoza, SpainDepartamento de Matemática Aplicada / IUMA, Universidad de Zaragoza, SpainDepartamento de Matemática Aplicada / CAPA, Universidad de Zaragoza, SpainDepartamento de Matemática Aplicada / IUMA, Universidad de Zaragoza, SpainThe problem of bivariate polynomial interpolation using Newton-type bases is examined, leading to the application of a generalized Kronecker matrix product. Algorithms for computing the coefficients of the interpolating polynomial are presented, along with conditions that ensure relative errors of the order of machine precision. A generalization of the classical recursion formula of divided differences in two dimensions is proposed for grids that generalize the standard rectangular layout. Numerical experiments demonstrate the high accuracy achieved by the proposed approach.https://www.aimspress.com/article/doi/10.3934/math.2025178high relative accuracybidiagonal decompositionstotally positive matricesbivariate interpolation |
| spellingShingle | Yasmina Khiar Esmeralda Mainar Eduardo Royo-Amondarain Beatriz Rubio High relative accuracy for a Newton form of bivariate interpolation problems AIMS Mathematics high relative accuracy bidiagonal decompositions totally positive matrices bivariate interpolation |
| title | High relative accuracy for a Newton form of bivariate interpolation problems |
| title_full | High relative accuracy for a Newton form of bivariate interpolation problems |
| title_fullStr | High relative accuracy for a Newton form of bivariate interpolation problems |
| title_full_unstemmed | High relative accuracy for a Newton form of bivariate interpolation problems |
| title_short | High relative accuracy for a Newton form of bivariate interpolation problems |
| title_sort | high relative accuracy for a newton form of bivariate interpolation problems |
| topic | high relative accuracy bidiagonal decompositions totally positive matrices bivariate interpolation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025178 |
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