Department of Mathematics
Multivariate quasi-interpolation schemes for dimension-splitting multiquadric
In this paper, we extend the multilevel univariate quasi-interpolation formula proposed in [A univariate quasi-multiquadric interpolation with better smoothness, Comput. Math. Appl., in press] to multidimensions using the dimension-splitting multiquadric (DSMQ) basis function approach. Our multivariate scheme is readily preformed on parallel computers. We show that the cost of finding the coefficient of the quasi-interpolant is 3dN on ℝd, and the work of direct evaluation of the quasi-interpolant can be reduced from 11N2 in 2D and 16N2 in 3D to ≈ 2N. A boundary padding technique can be employed to improve accuracy. Numerical results in 2D and 3D are both given. © 2003 Elsevier Inc. All rights reserved.
Dimension-splitting, Multidimensional, Multilevel, Multiquadric (MQ), Multivariate, Quasi-interpolation, Radial basis function (RBF)
Source Publication Title
Applied Mathematics and Computation
Link to Publisher's Edition
Ling, Leevan. "Multivariate quasi-interpolation schemes for dimension-splitting multiquadric." Applied Mathematics and Computation 161.1 (2005): 195-209.