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An adaptive greedy algorithm for solving large RBF collocation problems. (English) Zbl 1019.65093
The authors consider an adaptive greedy method, with slow linear convergence, in order to solve very large and at the same time, very general collocation problems. The method is a nonstandard one not directly aimed at a solution of the partial differential equation problems. In spite of this, the authors carry out some numerical results corresponding to the Dirichlet boundary value problem for the Poisson equation.

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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