Said-Ball-Vandermonde矩阵的精确计算
Accurate computations with Said-Ball-Vandermonde matrices
AI总结：
针对Said-Ball基替代幂基产生的广义Vandermonde矩阵，提出一种双对角分解算法，实现严格全正矩阵的高精度快速计算。
摘要：
考虑当幂基被Said-Ball基替代时产生的Vandermonde矩阵的推广。当节点位于区间(0,1)内时，这些矩阵是严格全正的。提出了一种计算这些Said-Ball-Vandermonde矩阵的双对角分解的算法，从而允许使用已知的用于由其双对角分解表示的全正矩阵的算法。该算法被证明是快速的，并且能够保证高相对精度。包括一些数值实验，说明了该算法的良好性能。
英文摘要：
A generalization of the Vandermonde matrices which arise when the power basis is replaced by the Said-Ball basis is considered. When the nodes are inside the interval (0,1), then those matrices are strictly totally positive. An algorithm for computing the bidiagonal decomposition of those Said-Ball-Vandermonde matrices is presented, which allows to use known algorithms for totally positive matrices represented by their bidiagonal decomposition. The algorithm is shown to be fast and to guarantee high relative accuracy. Some numerical experiments which illustrate the good behaviour of the algorithm are included.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
