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تسجيل مستخدم جديدFast Algorithms for the Multi-dimensional Jacobi Polynomial Transform
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We use the well-known observation that the solutions of Jacobis differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algorithm for computing multi-dimensional Jacobi polynomial transforms. More explicitly, it follows from this observation that the matrix corresponding to the discrete Jacobi transform is the Hadamard product of a numerically low-rank matrix and a multi-dimensional discrete Fourier transform (DFT) matrix. The application of the Hadamard product can be carried out via $O(1)$ fast Fourier transforms (FFTs), resulting in a nearly optimal algorithm to compute the multidimensional Jacobi polynomial transform.
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