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On Multivariate Interpolation
Author(s) -
Olver Peter J.
Publication year - 2006
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2006.00335.x
Subject(s) - interpolation (computer graphics) , multivariate statistics , mathematics , univariate , noncommutative geometry , multivariate interpolation , bilinear interpolation , multivariate analysis , nearest neighbor interpolation , calculus (dental) , pure mathematics , mathematical analysis , algebra over a field , statistics , computer science , motion (physics) , artificial intelligence , medicine , dentistry
A new approach to interpolation theory for functions of several variables is proposed. We develop a multivariate divided difference calculus based on the theory of noncommutative quasi‐determinants. In addition, intriguing explicit formulae that connect the classical finite difference interpolation coefficients for univariate curves with multivariate interpolation coefficients for higher dimensional submanifolds are established.