{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T21:41:27Z","timestamp":1762033287661},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,4,19]],"date-time":"2015-04-19T00:00:00Z","timestamp":1429401600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2016,2]]},"DOI":"10.1007\/s11075-015-9992-7","type":"journal-article","created":{"date-parts":[[2015,4,18]],"date-time":"2015-04-18T01:31:45Z","timestamp":1429320705000},"page":"273-292","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Multivariate polynomial interpolation with perturbed data"],"prefix":"10.1007","volume":"71","author":[{"given":"Claudia","family":"Fassino","sequence":"first","affiliation":[]},{"given":"Hans Michael","family":"M\u00f6ller","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,4,19]]},"reference":[{"key":"9992_CR1","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1016\/j.jsc.2008.05.002","volume":"43","author":"J Abbott","year":"2008","unstructured":"Abbott, J., Fassino, C., Torrente, M.: Stable border bases for ideals of points. J. Symbolic Comput. 43, 883\u2013894 (2008)","journal-title":"J. Symbolic Comput."},{"key":"9992_CR2","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/BF01890412","volume":"6","author":"C De Boor","year":"1990","unstructured":"De Boor, C., Ron, A.: On multivariate polynomial interpolation. Constr. Approx. 6, 287\u2013302 (1990)","journal-title":"Constr. Approx."},{"key":"9992_CR3","doi-asserted-by":"crossref","unstructured":"Buchberger, B., M\u00f6ller, H.M.: The construction of multivariate polynomials with preassigned zeros. In: Proceedings of EUROCAM \u201982, LNCS, vol. 144, pp 24\u201331. Springer, Berlin Heidelberg New York (1982)","DOI":"10.1007\/3-540-11607-9_3"},{"key":"9992_CR4","doi-asserted-by":"crossref","unstructured":"Cox, D., Little, J., O\u2019Shea, D.: Using algebraic geometry. Graduate texts in Mathematics, vol. 185. Springer, New York (1998)","DOI":"10.1007\/978-1-4757-6911-1"},{"key":"9992_CR5","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.jsc.2009.06.002","volume":"45","author":"C Fassino","year":"2010","unstructured":"Fassino, C.: Vanishing ideal of limited precision points. J. Symbolic Comput. 45, 19\u201337 (2010)","journal-title":"J. Symbolic Comput."},{"key":"9992_CR6","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1006\/jsco.1993.1051","volume":"16","author":"J Faug\u00e8re","year":"1993","unstructured":"Faug\u00e8re, J., Gianni, P., Lazard, D., Mora, T.: Efficient computation of zero-dimensional Gr\u00f6bner bases by change of ordering. J. Symbolic Comput. 16, 329\u2013344 (1993)","journal-title":"J. Symbolic Comput."},{"key":"9992_CR7","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1023\/A:1018981505752","volume":"12","author":"M Gasca","year":"2000","unstructured":"Gasca, M., Sauer, T.: Polynomial interpolation in several variables. Adv. Comput. Math. 12, 377\u2013410 (2000)","journal-title":"Adv. Comput. Math."},{"key":"9992_CR8","volume-title":"Matrix Computations","author":"GH Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. John Hopkins University Press, Baltimore (1996)","edition":"3rd edn."},{"key":"9992_CR9","doi-asserted-by":"crossref","first-page":"1566","DOI":"10.1016\/j.jsc.2008.11.010","volume":"44","author":"D Heldt","year":"2009","unstructured":"Heldt, D., Kreuzer, M., Pokutta, S., Poulisse, H.: Approximate computation of zero-dimensional polynomial ideals. J. Symbolic Comput. 44, 1566\u20131591 (2009)","journal-title":"J. Symbolic Comput."},{"key":"9992_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-70628-1","volume-title":"Computational Commutative Algebra 1","author":"M Kreuzer","year":"2000","unstructured":"Kreuzer, M., Robbiano, L.: Computational Commutative Algebra 1. Springer, Berlin (2000)"},{"key":"9992_CR11","doi-asserted-by":"crossref","unstructured":"Lakshman, Y.N.: On the complexity of computing Gr\u00f6bner bases for zero-dimensional polynomial ideals. Ph. D. Thesis. Rensselaer Polytechnic Institute, New York (1990)","DOI":"10.1007\/978-1-4612-0441-1_15"},{"key":"9992_CR12","unstructured":"Limbeck, J.: Computation of approximate border bases and applications. PhD Thesis. University of Passau (2013)"},{"key":"9992_CR13","doi-asserted-by":"crossref","unstructured":"Mora, T.: Solving polynomial equation systems II. Macaulay\u2019s Paradigm and Gr\u00f6bner Technology, Encyclopedia of Mathematics and its Applications, vol. 99. Cambridge University Press, Cambridge (2005)","DOI":"10.1017\/CBO9781107340954"},{"key":"9992_CR14","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/s002110050304","volume":"78","author":"T Sauer","year":"1997","unstructured":"Sauer, T.: Polynomial interpolation of minimal degree. Numer. Math. 78, 59\u201385 (1997)","journal-title":"Numer. Math."},{"key":"9992_CR15","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/s11075-007-9112-4","volume":"45","author":"T Sauer","year":"2007","unstructured":"Sauer, T.: Approximate varieties, approximate ideals, and dimension reduction. Numer. Algor. 45, 295\u2013313 (2007)","journal-title":"Numer. Algor."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-015-9992-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-015-9992-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-015-9992-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,23]],"date-time":"2019-08-23T18:40:57Z","timestamp":1566585657000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-015-9992-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,19]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,2]]}},"alternative-id":["9992"],"URL":"https:\/\/doi.org\/10.1007\/s11075-015-9992-7","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,19]]}}}