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An efficient algorithm for multivariate Maclaurin-Newton transformation. (English) Zbl 1284.65021

Summary: This paper presents explicit formulae for multivariate Maclaurin-Lagrange \(\mathcal M: K^{n_{1}\times n_{2} \times \ldots \times n_{d}} \to K^{n_{1} \times n_{2} \times \ldots \times n_{d}}\) and Maclaurin-Newton \(\mathcal P: K^{n_{1} \times n_{2} \times \ldots \times n_{d}} \to K^{n_{1} \times n_{2} \times \ldots \times n_{d}}\) transformations with respect to points whose coordinates form geometric sequences. Moreover, efficient algorithms for these transformations are given. Both of them perform computations with a running time of \(O(\prod^d_{j=1}n_j\cdot \log \prod^d_{j=1} n_j)+O(d\prod^d_{j=1}n_j)\).

MSC:

65D05 Numerical interpolation
65Y20 Complexity and performance of numerical algorithms
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References:

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