Multistep scattered data interpolation using compactly supported radial basis functions
Journal of Computational and Applied Mathematics - Special issue on scattered data
Computational test of approximation of functions and their derivatives by radial basis functions
Neural, Parallel & Scientific Computations
Fast Evaluation of Radial Basis Functions: Methods for Generalized Multiquadrics in $\RR^\protectn$
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
A multiquadric quasi-interpolation with linear reproducing and preserving monotonicity
Journal of Computational and Applied Mathematics
A kind of improved univariate multiquadric quasi-interpolation operators
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
| Hi-index | 0.10 |
In this paper, we propose a multilevel univariate quasi-interpolation scheme usingmultiquadric basis. It is practical as it does not require derivative values of the function being interpolated. It has a higher degree of smoothness than the original level-0 formula as it allows a shape parameter c=O(h). Our level-1 quasi-interpolation costs O(nlog@?n) flops to set up. It preserves strict convexity and monotonicity. When c=O(h), we prove the proposed scheme converges with a rate of O(h^2^.^5log@?h).Furthermore, if both |@?''(a)| and |@?''| are relatively small compared with @?@?''@?"~, the convergence rate will increase. We verify numerically that c = h is a good shape parameter to use for our method, hence we need not find the optimal parameter. For all test functions, both convergence speed and error are optimized for c between 0.5h and 1.5h. Our method can be generalized to a multilevel scheme; we include the numerical results for the level-2 scheme. The shape parameter of the level-2 scheme can be chosen between 2h to 3h.