The Matlab Radial Basis Function Toolbox

Radial Basis Function (RBF) methods are important tools for scattered data interpolation and for the solution of Partial Differential Equations in complexly shaped domains. The most straight forward approach used to evaluate the methods involves solving a linear system which is typically poorly conditioned. The Matlab Radial Basis Function toolbox features a regularization method for the ill-conditioned system, extended precision floating point arithmetic, and symmetry exploitation for the purpose of reducing flop counts of the associated numerical linear algebra algorithms.

[1]  S. Sarra,et al.  Multiquadric Radial Basis Function Approximation Methods for the Numerical Solution of Partial Differential Equations , 2009 .

[2]  Tien-Tsin Wong,et al.  Sampling with Hammersley and Halton Points , 1997, J. Graphics, GPU, & Game Tools.

[3]  Martin D. Buhmann,et al.  Radial Basis Functions , 2021, Encyclopedia of Mathematical Geosciences.

[4]  Holger Wendland,et al.  Scattered Data Approximation: Conditionally positive definite functions , 2004 .

[5]  R. E. Carlson,et al.  Improved accuracy of multiquadric interpolation using variable shape parameters , 1992 .

[6]  Elisabeth Larsson,et al.  Stable Computations with Gaussian Radial Basis Functions , 2011, SIAM J. Sci. Comput..

[7]  E. Kansa MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[8]  Samuel Cogar,et al.  An examination of evaluation algorithms for the RBF method , 2017 .

[9]  George Casella,et al.  The Early Use of Matrix Diagonal Increments in Statistical Problems , 1989, SIAM Rev..

[10]  Elisabeth Larsson,et al.  Stable computations with Gaussian radial basis functions in 2-D , 2009 .

[11]  Scott A. Sarra,et al.  A random variable shape parameter strategy for radial basis function approximation methods , 2009 .

[12]  Michael J. McCourt,et al.  Stable Evaluation of Gaussian Radial Basis Function Interpolants , 2012, SIAM J. Sci. Comput..

[13]  S. Sarra,et al.  Regularized symmetric positive definite matrix factorizations for linear systems arising from RBF interpolation and differentiation , 2014 .

[14]  Scott A. Sarra,et al.  Radial basis function approximation methods with extended precision floating point arithmetic , 2011 .

[15]  G. Fasshauer,et al.  STABLE EVALUATION OF GAUSSIAN RBF INTERPOLANTS , 2011 .

[16]  Gregory E. Fasshauer,et al.  Meshfree Approximation Methods with Matlab , 2007, Interdisciplinary Mathematical Sciences.

[17]  A. Cheng,et al.  Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method , 2007 .

[18]  S. R. Searle,et al.  On Deriving the Inverse of a Sum of Matrices , 1981 .

[19]  E. Kansa Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .