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Wong, Wing Hung

On constrained multivariate splines and their approximations. (English) Zbl 0553.41028

Numer. Math. 43, 141-152 (1984).
The variational formulation of multivariate spline functions is generalized to include cases where the function has to satisfy inequality constraints such as positivity and convexity. The author gives condition for existence and uniqueness of a solution, and shows that an approximation to the solution can be obtained by solving the variational problem in a finite dimensional subspace. Both for interpolation and smoothing problems conditions for convergence and error estimates of the approximations are given. Two special examples, as ”volume matching” problem and ”the one-sided thin plate spline”, are given as an illustration of the general theory.
Reviewer: A.Bleyer

Cited in 6 Documents

MSC:

41A29 Approximation with constraints
41A15 Spline approximation
65N15 Error bounds for boundary value problems involving PDEs
41A63 Multidimensional problems

Keywords:

multivariate spline functions; examples; volume matching; the one-sided thin plate spline
PDFBibTeX XMLCite
\textit{W. H. Wong}, Numer. Math. 43, 141--152 (1984; Zbl 0553.41028)
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References:

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