Fast Solution of Confluent Vandermonde Linear Systems
暂无分享,去创建一个
It is shown that the solution of confluent Vandermonde linear systems can be obtained by the Hermite evaluation of rational functions, which can actually be converted to the Hermite evaluation of two polynomials. Based on this result, divide and conquer methods are used to construct a fast algorithm for confluent Vandermonde linear systems. If fast polynomial multiplication and division (fast Fourier transform (FFT)) are used, the algorithm needs only $O(n \log n \log p)$ operations.
[1] Lothar Reichel,et al. Chebyshev-Vandermonde systems , 1991 .
[2] V. Pereyra,et al. On the construction of discrete approximations to linear differential expressions. , 1967 .
[3] Victor Y. Pan,et al. Polynomial division and its computational complexity , 1986, J. Complex..
[4] Cédric J. Demeure. Fast QR factorization of Vandermonde matrices , 1989 .
[5] Å. Björck,et al. Solution of Vandermonde Systems of Equations , 1970 .