| 一类非线性分形插值曲面的构造与性质 |
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| 引用本文： | 姜伟.一类非线性分形插值曲面的构造与性质[J].中北大学学报,2012(1):56-59. |
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| 作者姓名： | 姜伟 |
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| 作者单位： | 太原理工大学数学学院 |
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| 摘 要： | 讨论了二元连续函数振幅与变差的性质,并构造了一类非线性多参数迭代函数系;证明了在一定条件下吸引子的唯一性和分形插值曲面的存在性,利用连续函数变差的性质研究了所构造的分形插值曲面的维数,并给出了此类分形插值曲面计盒维数的计算公式.
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| 关 键 词： | 非线性迭代函数系 分形插值 连续性 变差 维数 |
Construction and Properties of a Class of Nonlinear Fractional Interpolation Surface |
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| JIANG Wei.Construction and Properties of a Class of Nonlinear Fractional Interpolation Surface[J].Journal of North University of China,2012(1):56-59. |
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| Authors: | JIANG Wei |
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| Affiliation: | JIANG Wei(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China) |
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| Abstract: | The properties of amplitude and variation of the binary continuous function was discussed,and a class of nonlinear iterated function system of multiple arbitrary parameters was constructed.The uniqueness of the attractor and the existence of the fractal interpolation surface was proved under certain conditions.By using the properties of variation of the continuous function,the box-dimension of the constructed fractal interpolation surface was studied and the calculation formula of the box-dimension was given. |
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| Keywords: | nonlinear iterated function system fractional interpolation continuity variation box dimension |
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