Fast Solution of Confluent Vandermonde Linear Systems
Hao Lu · SIAM Journal on Matrix Analysis and Applications · 1994
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.