Uniqueness of solutions in multivariate Chebyshev approximation problems
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| Title: | Uniqueness of solutions in multivariate Chebyshev approximation problems |
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| Authors: | Vera Roshchina, Nadezda Sukhorukova, Julien Ugon |
| Publication Year: | 2024 |
| Subject Terms: | Mathematical sciences, Applied mathematics, Numerical and computational mathematics, Pure mathematics, ALGORITHM, Chebyshev approximation, Mathematics, Applied, Multivariate polynomial approximation, Operations Research & Management Science, Physical Sciences, Science & Technology, Technology, Uniqueness of solutions |
| Description: | We study the solution set to multivariate Chebyshev approximation problem, focussing on the ill-posed case when the uniqueness of solutions can not be established via strict polynomial separation. We obtain an upper bound on the dimension of the solution set and show that nonuniqueness is generic for ill-posed problems on discrete domains. Moreover, given a prescribed set of points of minimal and maximal deviation we construct a function for which the dimension of the set of best approximating polynomials is maximal for any choice of domain. We also present several examples that illustrate the aforementioned phenomena, demonstrate practical application of our results and propose a number of open questions. |
| Document Type: | article in journal/newspaper |
| Language: | unknown |
| Relation: | http://hdl.handle.net/10779/DRO/DU:24165987.v1; https://figshare.com/articles/journal_contribution/Uniqueness_of_solutions_in_multivariate_Chebyshev_approximation_problems/24165987 |
| Availability: | http://hdl.handle.net/10779/DRO/DU:24165987.v1 https://figshare.com/articles/journal_contribution/Uniqueness_of_solutions_in_multivariate_Chebyshev_approximation_problems/24165987 |
| Rights: | All Rights Reserved |
| Accession Number: | edsbas.5113E271 |
| Database: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | We study the solution set to multivariate Chebyshev approximation problem, focussing on the ill-posed case when the uniqueness of solutions can not be established via strict polynomial separation. We obtain an upper bound on the dimension of the solution set and show that nonuniqueness is generic for ill-posed problems on discrete domains. Moreover, given a prescribed set of points of minimal and maximal deviation we construct a function for which the dimension of the set of best approximating polynomials is maximal for any choice of domain. We also present several examples that illustrate the aforementioned phenomena, demonstrate practical application of our results and propose a number of open questions. |
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