I have been studying Fourier matrices and have used the following code to compute a simple polynomial multiplication:
A = {3, 7, 0, 0}
B = {-1, 2, 1, 0}
A1 = 2 FourierMatrix[4] . A
B1 = 2 FourierMatrix[4] . B
.5 InverseFourier[A1*B1]
the results are as expected ({-3., -1., 17., 7.}) but when I try to multiply larger polynomials such as
A = {3, 7, 0, 1,0,0,0,0}
B = {-1, 2, 1, 0,0,0,0,0}
A1 = sqrt[8]FourierMatrix[8] . A
B1 = sqrt[8]FourierMatrix[8] . B
1/8InverseFourier[A1*B1]
I get wild results that don't seem to reflect the correct coefficients. What am I missing?
