Least squares approximation by radial functions
SIAM Journal on Mathematical Analysis
Generalized Hermite interpolation via matrix-valued conditionally positive definite functions
Mathematics of Computation
On unsymmetric collocation by radial basis functions
Applied Mathematics and Computation
Least squares scattered data fitting by truncated SVDs
Applied Numerical Mathematics - Applied and computational mathematics: Selected papers of the third panamerican workshop Trujillo, Peru, 24-28 April 2000
Large scale least squares scattered data fitting
Applied Numerical Mathematics
Overlapping domain decomposition method by radial basis functions
Applied Numerical Mathematics
Radial Basis Functions
Adaptive radial basis function methods for time dependent partial differential equations
Applied Numerical Mathematics
Adaptive Atmospheric Modeling: Scientific Computing at Its Best
Computing in Science and Engineering
Domain decomposition by radial basis functions for time dependent partial differential equations
ACST'06 Proceedings of the 2nd IASTED international conference on Advances in computer science and technology
Adaptive Node Refinement Collocation Method for Partial Differential Equations
ENC '06 Proceedings of the Seventh Mexican International Conference on Computer Science
Least squares collocation solution of elliptic problems in general regions
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
Computers & Mathematics with Applications
Preconditioning for radial basis functions with domain decomposition methods
Mathematical and Computer Modelling: An International Journal
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We consider a collocation method using radial functions for the solution of partial differential equations in irregular domains. We use a regularised least squares approach to solve the potentially ill-conditioned problems that may arise. This meshless method is easy to implement and eliminates most of the problems that mesh oriented methods have with irregular boundaries and complicated domains. When solving, also, for the position and shape parameters of the radial functions we obtain an adaptive, albeit non-linear, method. In this case, the resulting problem is a separable non-linear least squares one that can be efficiently solved by the Variable Projection method.