Using a fast multipole method to accelerate spline evaluations

In considering the problem of interpolating scattered data using spline methods, the authors present a general framework for using the multipole method to accelerate spline evaluations. The article also illustrates the efficiency and accuracy of the fast multipole algorithm for the 2D vector spline.

[1]  V. Rokhlin.  Rapid solution of integral equations of classical potential theory , 1985 .

[2]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[3]  Vladimir Rokhlin,et al.  A Fast Algorithm for the Numerical Evaluation of Conformal Mappings , 1989 .

[4]  Feng Zhao,et al.  The Parallel Multipole Method on the Connection Machine , 1991, SIAM J. Sci. Comput..

[5]  A. Brandt.  Multilevel computations of integral transforms and particle interactions with oscillatory kernels , 1991 .

[6]  L. Amodei,et al.  A Vector Spline Approximation With Application to Meteorology , 1991, Curves and Surfaces.

[7]  R. Beatson,et al.  Fast evaluation of radial basis functions: I , 1992 .

[8]  Christopher R. Anderson,et al.  An Implementation of the Fast Multipole Method without Multipoles , 1992, SIAM J. Sci. Comput..

[9]  J. Boyd.  Multipole expansions and pseudospectral cardinal functions: A new generalization of the fast fourier transform , 1992 .

[10]  Frank Thomson Leighton,et al.  Preconditioned, Adaptive, Multipole-Accelerated Iterative Methods for Three-Dimensional First-Kind Integral Equations of Potential Theory , 1994, SIAM J. Sci. Comput..

[11]  Fast Evaluation of Splines Using Poisson Formula , 1994 .

[12]  C. Leonard Berman.  Grid-Multipole Calculations , 1995, SIAM J. Sci. Comput..

[13]  John A. Board,et al.  Fast Fourier Transform Accelerated Fast Multipole Algorithm , 1996, SIAM J. Sci. Comput..

[14]  R. Beatson,et al.  Fast evaluation of radial basis functions : methods for two-dimensional polyharmonic splines , 1997 .

[15]  David Suter,et al.  Fast evaluation of vector splines in two dimensions , 1997 .

[16]  Richard K. Beatson,et al.  Fast Evaluation of Radial Basis Functions: Moment-Based Methods , 1998, SIAM J. Sci. Comput..