High accuracy multiquadric quasi-interpolation

Jiang, Ziwu; Wang, Ren-Hong; Zhu, Chun‐Gang; Xu, Min

doi:10.1016/j.apm.2010.11.022

Cited by 19 publications

(30 citation statements)

References 23 publications

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“…(6) and (7) is denoted by 2 . For more details about the properties and accuracy of and 2 , one can see [19].…”

Section: The Mq Quasi-interpolation Schemementioning

confidence: 99%

“…By using MQ quasiinterpolation scheme, we can avoid this problem, whereas the approximation order is not good. Therefore, Jiang et al [19] defined two MQ quasi-interpolation operators denoted as and 2 which pose the advantages of RBFs interpolation and MQ quasi-interpolation scheme. The process of MQ quasiinterpolation of and 2 are as follows that is described in [19].…”

Section: The Mq Quasi-interpolation Schemementioning

confidence: 99%

“…Beatson and Powell [2] and Wu and Schaback [29] proposed other univariate MQ quasi-interpolations. Recently, Jiang et al [19] have introduced a new multi-level univariate MQ quasi-interpolation approach with high approximation order compared with initial MQ quasi-interpolation scheme, namely as and 2 . This approach is based on inverse multiquadric (IMQ) RBF interpolation, and Wu and Schaback's MQ quasi-interpolation operator that have the advantages of high approximation order.…”

Section: Introductionmentioning

confidence: 99%

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Improvement Of The Multiquadric Quasi-interpolation Lw2

Sarboland¹,

Aminataei²

2014

J. Math. Computer Sci.

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In this paper, we improve the multiquadric (MQ) quasi-interpolation operator 2 . The operator 2 is based on inverse multiquadric radial basis function (IMQ-RBF) interpolation, and Wu and Schaback's MQ quasi-interpolation operator . In definition process of the quasi-interpolation 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 2 . Numerical experiments demonstrate that the proposed MQ quasi-interpolation scheme is valid.

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“…(6) and (7) is denoted by 2 . For more details about the properties and accuracy of and 2 , one can see [19].…”

Section: The Mq Quasi-interpolation Schemementioning

confidence: 99%

Section: The Mq Quasi-interpolation Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improvement Of The Multiquadric Quasi-interpolation Lw2

Sarboland¹,

Aminataei²

2014

J. Math. Computer Sci.

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show abstract

“…By using MQ quasiinterpolation scheme, we can avoid this problem, whereas the approximation order is not good. Therefore, Jiang et al [16] defined two MQ quasi-interpolation operators denoted as …”

Section: The Mq Quasi-interpolation Schemementioning

confidence: 99%

“…Also, Xiao et al [25] presented the numerical method based on Chen and Wu's method for solving the third-order KdV equation. Recently, Jiang et al [16] have introduced a new multi-level univariate MQ quasi-interpolation approach with high approximation order compared with initial MQ quasi-interpolation scheme. This approach is based on inverse multiquadric (IMQ) RBF interpolation, and Wu and Schaback's MQ quasi-interpolation operator D L that have the advantages of high approximation order.…”

Section: Introductionmentioning

confidence: 99%

Integrated High Accuracy Multiquadric Quasi-interpolation Scheme For Solving The Nonlinear Klein-gordon Equation

Sarboland¹,

Aminataei²

2015

J. Math. Computer Sci.

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A collocation scheme based on the use of the multiquadric quasi-interpolation operator 2 W L , integrated radial basis function networks (IRBFNs) method and three order finite difference method is applied to the nonlinear Klein-Gordon equation. In the present scheme, the three order finite difference method is used to discretize the temporal derivative and the integrated form of the multiquadric quasi-interpolation scheme is used to approximate the unknown function and its spatial derivatives. Several numerical experiments are provided to show the efficiency and the accuracy of the given method.

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A new multiquadric quasi‐interpolation operator with interpolation property

2013

Math Methods in App Sciences

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In this article, we discuss a class of multiquadric quasi‐interpolation operator that is primarily on the basis of Wu–Schaback's quasi‐interpolation operator scriptLscriptD and radial basis function interpolation. The proposed operator possesses the advantages of linear polynomial reproducing property, interpolation property, and high accuracy. It can be applied to construct flexible function approximation and scattered data fitting from numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd.

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High accuracy multiquadric quasi-interpolation

Cited by 19 publications

References 23 publications

Improvement Of The Multiquadric Quasi-interpolation Lw2

Improvement Of The Multiquadric Quasi-interpolation Lw2

Integrated High Accuracy Multiquadric Quasi-interpolation Scheme For Solving The Nonlinear Klein-gordon Equation

A new multiquadric quasi‐interpolation operator with interpolation property

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