Improvement of the Multiquadric Quasi-interpolation \(L_{w_2} \)

Volume 11, Issue 1, pp 13-21 http://dx.doi.org/10.22436/jmcs.011.01.02

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Authors

Maryam Sarboland - Faculty of Mathematics, Department of Applied Mathematics, K. N. Toosi University of Technology, P.O. Box: 15418-49611, Tehran, Iran. Azim Aminataei - Faculty of Mathematics, Department of Applied Mathematics, K. N. Toosi University of Technology, P.O. Box: 15418-49611, Tehran, Iran.

Abstract

In this paper, we improve the multiquadric (MQ) quasi-interpolation operator \(L_{w_2 }\). The operator \(L_{w_2 }\) is based on inverse multiquadric radial basis function (IMQ-RBF) interpolation, and Wu and Schaback's MQ quasi-interpolation operator \(L_D\). In definition process of the quasi-interpolation \(L_{w_2 }\), the second derivative of function is used that approximated by center finite difference. In this paper, we use compact finite difference for approximation of the second derivative and increase accuracy of quasi-interpolation \(L_{w_2 }\). Numerical experiments demonstrate that the proposed MQ quasi-interpolation scheme is valid.

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Keywords

• Radial basis function
• Multiquadric quasi-interpolation
• Inverse multiquadric
• Compact finite difference.

MSC

•  65D05
•  65D10
•  65M55
•  65M70

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