| MULTIVARIATE FOURIER TRANSFORM METHODS OVER SIMPLEX AND SUPER-SIMPLEX DOMAINS |
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| 作者姓名： | Jiachang Sun |
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| 作者单位： | Jiachang Sun，Institute of Software，Chinese Academy of Sciences，Beijing 100080，China |
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| 基金项目： | This work was partly supported by National Science Foundation of China （No. 10431050 and 60573023）, the Major Basic Project of China （2005CB321702） and by Natural Science Foundation of United States （No. CCF0305666） during the author＇s visit at University of Colorado at Boulder. |
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| 摘 要： | In this paper we propose the well-known Fourier method on some non-tensor productdomains in R~d, inclding simplex and so-called super-simplex which consists of (d 1)!simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a parallelhexagon and a parallel quadrilateral dodecahedron, respectively. We have extended mostof concepts and results of the traditional Fourier methods on multivariate cases, such asFourier basis system, Fourier series, discrete Fourier transform (DFT) and its fast algorithm(FFT) on the super-simplex, as well as generalized sine and cosine transforms (DST, DCT)and related fast algorithms over a simplex. The relationship between the basic orthogonalsystem and eigen-functions of a Laplacian-like operator over these domains is explored.
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| 关 键 词： | 多元傅立叶转换 多元正弦余弦函数 算子 基本正交系统 |
| 收稿时间： | 2006-03-01 |
| 修稿时间： | 2006-03-01 |
MULTIVARIATE FOURIER TRANSFORM METHODS OVER SIMPLEX AND SUPER-SIMPLEX DOMAINS |
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| Jiachang Sun.MULTIVARIATE FOURIER TRANSFORM METHODS OVER SIMPLEX AND SUPER-SIMPLEX DOMAINS[J].Journal of Computational Mathematics,2006,24(3):305-322. |
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| Authors: | Jiachang;Sun |
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| Abstract: | In this paper we propose the well-known Fourier method on some non-tensor product domains in R~d, inclding simplex and so-called super-simplex which consists of (d 1)! simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a parallel hexagon and a parallel quadrilateral dodecahedron, respectively. We have extended most of concepts and results of the traditional Fourier methods on multivariate cases, such as Fourier basis system, Fourier series, discrete Fourier transform (DFT) and its fast algorithm (FFT) on the super-simplex, as well as generalized sine and cosine transforms (DST, DCT) and related fast algorithms over a simplex. The relationship between the basic orthogonal system and eigen-functions of a Laplacian-like operator over these domains is explored. |
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| Keywords: | Multivariate Fourier transform Simplex and super-simplex Multivariate sine cosine functions Eigen-decomposition for Laplacian-like operator Multivariate fast Fourier transform |
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