Premium
Spline Interpolation under Two‐Sided Restrictions on the Derivatives
Author(s) -
Schmidt J. W.,
Hess W.
Publication year - 1989
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.19890691012
Subject(s) - interpolation (computer graphics) , mathematics , quadratic equation , spline interpolation , curvature , spline (mechanical) , regular polygon , inverse quadratic interpolation , monotone cubic interpolation , domain (mathematical analysis) , bilinear interpolation , nearest neighbor interpolation , mathematical analysis , geometry , computer science , computer graphics (images) , physics , statistics , animation , thermodynamics
In the present paper the interpolation of data sets is considered under two‐sided constraints on the derivatives. Thus, e.g., the interpolants may be convex on some pieces of the domain and concave on others. For solving these interpolation problems quadratic and cubic splines are used. In extending earlier results necessary and sufficient existence conditions are derived as well as numerical procedures for determining interpolants with minimal curvature.