@TechReport{	  it:2009-020,
  author	= {Bengt Fornberg and Elisabeth Larsson and Natasha Flyer},
  title		= {Stable Computations with {G}aussian Radial Basis Functions
		  in {2-D}},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2009},
  number	= {2009-020},
  month		= aug,
  abstract	= {Radial basis function (RBF) approximation is an extremely
		  powerful tool for representing smooth functions in
		  non-trivial geometries, since the method is meshfree and
		  can be spectrally accurate. A perceived practical obstacle
		  is that the interpolation matrix becomes increasingly
		  ill-conditioned as the RBF shape parameter becomes small,
		  corresponding to flat RBFs. Two stable approaches that
		  overcome this problem exist, the Contour-Pad\'e method and
		  the RBF-QR method. However, the former is limited to small
		  node sets and the latter has until now only been formulated
		  for the surface of the sphere. This paper contains an
		  RBF-QR formulation for planar two-dimensional problems. The
		  algorithm is perfectly stable for arbitrarily small shape
		  parameters and can be used for up to a thousand node points
		  in double precision and for several thousand node points in
		  quad precision. A sample MATLAB code is provided.}
}