{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:37:25Z","timestamp":1787330245052,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2001,1]]},"abstract":"<jats:p>\n                    In this paper, we apply techniques from the theory of ideals and varieties in algebraic geometry to study the geometric structure of a properly posed set of nodes (or PPSN, for short) for multivariate Lagrange interpolation along an algebraic hypersurface. We provide a hyperplane-superposition process to construct the PPSN for interpolation along an algebraic hypersurface, and as a result, we offer a clear understanding of the geometric structure of the PPSN for multivariate Lagrange interpolation in C\n                    <jats:sup>s<\/jats:sup>\n                    .\n                  <\/jats:p>","DOI":"10.1137\/s0036142999361566","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"587-595","source":"Crossref","is-referenced-by-count":16,"title":["Properly Posed Sets of Nodes for Multivariate Lagrange Interpolation in\n                    <i>\n                      C\n                      <sup>s<\/sup>\n                    <\/i>"],"prefix":"10.1137","volume":"39","author":[{"given":"Xue-Zhang","family":"Liang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chun-Mei","family":"L\u00fc","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ren-Zhong","family":"Feng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"Chui, C. K. and M. J. Lai,\n                      Vandermonde determinant and Lagrange interpolation in Rs\n                      , in Nonlinear and Convex Analysis, B. L. Lin and S. Simons, eds., Marcel Dekker, New York, 1987, 23\u201336."},{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0714050"},{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0714050"},{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0714050"},{"key":"R1","unstructured":"Liang, X. Z.\n                      On the interpolation and approximation in several variables\n                      , Postgraduate Thesis, Jilin University, Changchun, 1965."},{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0714050"},{"key":"R1","unstructured":"Liang, X. Z. and L\u00fc, C. M.\n                      Properly posed set of nodes for bivariate Lagrange interpolation\n                      , in Approximation Theory IX, Vol. 2: Computational Aspect, C. K. Chui and L. L. Schumaker eds., Vanderbilt University Press, (1998) p. 189\u2013196."},{"key":"R1","unstructured":"D. Cox, J. Little and D. O\u2019shea,\n                      Ideals, Varieties, and Algorithms\n                      , Springer\u2010Verlag, New York, 1992."},{"key":"R1","unstructured":"M. Gasca,\n                      Multivariate polynomial interpolation\n                      , in Computation of Curves and Surfaces, Kluwer, 1990, p. 215\u2013236."},{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0714050"},{"key":"R2","unstructured":"C. K. Chui and M. J. Lai,\n                      Vandermonde determinant and Lagrange interpolation in Rs\n                      , in Nonlinear and Convex Analysis, B. L. Lin and S. Simon, eds., Marcel Dekker, New York, 1987, pp. 23\u201336."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0714050"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02571803"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01399308"},{"key":"R6","unstructured":"X. Z. Liang,\n                      On the interpolation and approximation in several variables\n                      , Postgraduate Thesis, Jilin University, Changchun, China, 1965."},{"key":"R7","first-page":"385","volume":"32","author":"Liang Xue","year":"1989","journal-title":"Sci. China Ser. A"},{"key":"R8","unstructured":"Xue\u2010Zhang Liang, Chun\u2010Mei Lu, Properly posed set of nodes for bivariate Lagrange interpolation, Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, 1998, 189\u20131961744407"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2693-0"},{"key":"R10","unstructured":"M. Gasca, Multivariate polynomial interpolation, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 307, Kluwer Acad. Publ., Dordrecht, 1990, 215\u201323691k:65028"},{"key":"R11","first-page":"27","volume":"1","author":"Liang X. Z.","year":"1979","journal-title":"Jilin Daxue Xuebao"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0036142999361566","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:54:01Z","timestamp":1787327641000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0036142999361566"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2001,1]]}},"alternative-id":["10.1137\/S0036142999361566"],"URL":"https:\/\/doi.org\/10.1137\/s0036142999361566","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,1]]}}}