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Pure Mathematics 2023
定义于椭球面上的多元切触插值问题研究
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Abstract:
以定义于平面代数曲线上的切触插值研究结果为基础，对定义于椭球面上的切触插值问题进行了研究。给出了定义于椭球面上的切触插值和插值正则性条件组问题提法，对插值条件组的拓扑结构进行了较为深入的研究，得到了定义于椭球面上的切触插值正则条件组的判定定理以及迭加构造方法，最后给出了实验算例验证了算法的有效性。
Based on the research results of tangent interpolation defined on planar algebraic curves, the problem of tangent interpolation defined on an ellipsoid was studied. The formulation of the tan-gent interpolation problem defined on an ellipsoid and the regularization condition set for inter-polation were given. The topological structure of the interpolation condition set was thoroughly studied, and the decision theorem and superposition method for the tangent interpolation regu-larization condition set defined on an ellipsoid were obtained. Finally, experimental examples were provided to verify the effectiveness of the algorithm.
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