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A multiquadric quasi-interpolation with linear reproducing and preserving monotonicity |
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| Authors: | Ronghua Chen Xuli Han |
| Institution: | a School of Mathematical Science and Computing Technology, Central South University, Changsha, Hunan, 410083, PR China b School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, Hunan, 411201, PR China c Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematics, Fudan University, Shanghai, 200433, PR China |
| Abstract: | In this paper, we develop a multiquadric (MQ) quasi-interpolation which has the properties of linear reproducing and preserving monotonicity. Moreover, we give its approximation error by theoretic analysis and illustrate the effect by means of two examples. One of the examples is to approach the linear combination of two sine functions with different frequencies. Another is to approximate a function with discontinuity. From the results of the examples, we believe that the present MQ quasi-interpolation is feasible. |
| Keywords: | Radial basis function Multiquadric quasi-interpolation Shape parameter Linear reproducing Preserving monotonicity |
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