Sparse Polynomial Hermite Interpolation
Sparse Polynomial Hermite Interpolation
复制标题
DOI：
10.1145/3476446.3535501
复制
发表时间：
2022-07
期刊：
影响因子：
--
通讯作者：
E. Kaltofen
中科院分区：
文献类型：
--
作者：
E. Kaltofen
We present Hermite polynomial interpolation algorithms that for a sparse univariate polynomial f with coefficients from a field compute the polynomial from fewer points than the classical algorithms. If the interpolating polynomial f has t terms, our algorithms, which use randomiization, require argument/value triples （Wi，f（Wi），F'（Wi））for I = 0，...，T +↾（t + 1）/2↿ -1，其中W随机采样W，正确输出的可能性为决定从F'的度数中，我们表示我们的算法对多种方面的多项式，较高的衍生物和稀疏性相对于Chebyshev多项式碱基。良好的值数量。返回不正确的输出。
We present Hermite polynomial interpolation algorithms that for a sparse univariate polynomial f with coefficients from a field compute the polynomial from fewer points than the classical algorithms. If the interpolating polynomial f has t terms, our algorithms, which use randomization, require argument/value triples (wi,f(wi),f'(wi)) for i=0, ..., t + ↾(t+1)/2↿ - 1, where w is randomly sampled and the probability of a correct output is determined from a degree bound for f. With f' we denote the derivative of f. Our algorithms generalize to multivariate polynomials, higher derivatives and sparsity with respect to Chebyshev polynomial bases. We have algorithms that can correct errors in the points by oversampling at a limited number of good values. If an upper bound B ≥ t for the number of terms is given, our algorithms use a randomly selected w and, with high probability, t/2 + B triples, but then never return an incorrect output.