Multivariate approximation by PDE splines. (English) Zbl 1146.65020
Starting from the data point set characterizing a surface and from the elliptic partial differential equation (PDE) that describes a certain physical phenomenon the authors present the approximation method managing the fitting of the data points by least squares and the solution of the PDE. The so-called PDE spline is the solution of a minimization problem in a convex set in a Sobolev space. This solution is obtained using the method of Lagrangian multipliers.
The main purpose of this paper is to prove the existence, the uniqueness and the convergence of the solution in question. The authors present an example to illustrate this fitting method employing the finite-difference discretization to solve PDEs numerically.
The main purpose of this paper is to prove the existence, the uniqueness and the convergence of the solution in question. The authors present an example to illustrate this fitting method employing the finite-difference discretization to solve PDEs numerically.
Reviewer: Jacek Gilewicz (Marseille)
MSC:
| 65D10 | Numerical smoothing, curve fitting |
| 65D07 | Numerical computation using splines |
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
| 65D15 | Algorithms for approximation of functions |
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