Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 195-209 |
Number of pages | 15 |
Journal | Applied Mathematics and Computation |
Volume | 161 |
Issue number | 1 |
DOIs | |
Publication status | Published - 4 Feb 2005 |
Scopus Subject Areas
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- Dimension-splitting
- Multidimensional
- Multilevel
- Multiquadric (MQ)
- Multivariate
- Quasi-interpolation
- Radial basis function (RBF)