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Interpolation with tensor product splines subject to derivative constraints
Author(s) -
Walther Marion
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.199807815128
Subject(s) - mathematics , tensor product , interpolation (computer graphics) , piecewise , bicubic interpolation , grid , spline (mechanical) , constant (computer programming) , product (mathematics) , pure mathematics , derivative (finance) , mathematical analysis , order (exchange) , spline interpolation , geometry , bilinear interpolation , computer science , physics , motion (physics) , statistics , finance , financial economics , economics , thermodynamics , programming language , artificial intelligence
In this paper restricted interpolations of data sets (x i , y j , z i, j ), i = 0,…, n, j = 0,…, m, on the rectangular grid Δ × Σ = {x 0 <… < x n } × {yo <… < ym} are handled using biquadratic C 1 and bicubic C 2 splines on refined grids. The constraints on the first order derivatives are piecewise constant with respect to the original grid Δ × Σ. If the refinement of the grids are chosen adaptively, the existence of restricted interpolants can be assured for bounds strictly compatible with the data.