Interpolation of Lipschitz functions
This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario...
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| Published in | Journal of computational and applied mathematics Vol. 196; no. 1; pp. 20 - 44 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.11.2006
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-0427 1879-1778 |
| DOI | 10.1016/j.cam.2005.08.011 |
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| Abstract | This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function
f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on
f, and thus translates into reliable learning of
f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data. |
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| AbstractList | This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function
f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on
f, and thus translates into reliable learning of
f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data. This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on f, and thus translates into reliable learning of f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data. |
| Author | Beliakov, Gleb |
| Author_xml | – sequence: 1 givenname: Gleb surname: Beliakov fullname: Beliakov, Gleb email: gleb@deakin.edu.au organization: School of Information Technology, Deakin University, 221 Burwood Hwy, Burwood, 3125, Australia |
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| Cites_doi | 10.1007/BF02837633 10.1016/0041-5553(78)90035-6 10.1137/0709036 10.1016/0885-064X(86)90009-9 10.1007/978-1-4757-3200-9 10.1007/978-1-4615-4677-1 10.1016/0041-5553(71)90017-6 10.1007/BF01395972 10.1016/0041-5553(72)90115-2 10.1007/978-94-011-2759-2 10.1080/00207169508804450 10.1002/int.10120 10.1016/S0305-0548(02)00082-5 10.1007/PL00009366 10.1016/S0898-1221(97)00087-4 10.1023/A:1020256900863 10.1080/02331930310001611556 10.1016/0041-5553(76)90069-0 10.1145/116873.116880 10.1007/BF00229304 |
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| Keywords | Optimal interpolation Multivariate approximation 41A30 41A63 65D05 41A50 Lipschitz approximation 41A05 Scattered data interpolation Central algorithm 65D05; 41A05; 41A30; 41A50; 41A63 Finite volume method Numerical approximation Radial basis function Multivariate interpolation Numerical analysis Scattered data interpolation; Lipschitz approximation; Optimal interpolation; Central algorithm; Multivariate approximation Efficiency Lipschitz function |
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| SubjectTerms | Approximations and expansions Central algorithm Exact sciences and technology Lipschitz approximation Mathematical analysis Mathematics Multivariate approximation Numerical analysis Numerical analysis. Scientific computation Numerical approximation Optimal interpolation Scattered data interpolation Sciences and techniques of general use |
| Title | Interpolation of Lipschitz functions |
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