Properly posed sets of nodes for multivariate lagrange interpolation in C-s

Authors
Liang, XZ Lu, CM Feng, RZ
Citation
Xz. Liang et al., Properly posed sets of nodes for multivariate lagrange interpolation in C-s, SIAM J NUM, 39(2), 2001, pp. 587-595
Citations number
10
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN journal
00361429 → ACNP
Volume
39
Issue
2
Year of publication
2001
Pages
587 - 595
Database
ISI
SICI code
0036-1429(20010708)39:2<587:PPSONF>2.0.ZU;2-I
Abstract
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 a long an algebraic hypersurface. We provide a hyperplane-superposition proce ss 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-s.