Fast least squares solution of Vandermonde systems of equations
C.J. Demeure, Louis L. Scharf · International Conference on Acoustics, Speech, and Signal Processing · 2003
The authors introduce a fast algorithm for computing the QR factors of a complex column Vandermonde matrix V. The complexity of the algorithm is 5 mn+7 n/sup 2//2+O(m), where m is the number of rows in V and n is the number of columns (they assume that m>n). The matrices Q and R can be computed independently if desired. Such an algorithm allows an important saving when solving such systems in the least-squares sense, as for example when estimating the magnitude and phase of damped exponentials in the least-squares version of the Prony method.>