FFT itérative, FFT parallèle Calcul des premières dérivées d

𝐴mir (𝑥) =
𝑛−1
𝑗=0 𝑎𝑛−1−𝑗𝑥𝑗𝐴(𝑥) =
𝑛−1
𝑗=0 𝑎𝑗𝑥𝑗
𝐴 𝐵 𝑛
10𝑛 𝐶 𝐴
𝐵
𝐶={𝑥+𝑦∣𝑥∈𝐴&𝑦∈𝐵}.
𝐶 𝐶
𝐴 𝐵
𝑂(𝑛log 𝑛)
𝑧0, 𝑧1, . . . , 𝑧𝑛−1
𝑃
𝑛
𝑂(𝑛log2𝑛)
𝑃= (𝑎0, 𝑎1, 𝑎2, 𝑎3, 𝑎4, 𝑎5, 𝑎6, 𝑎7)
𝑛
𝑛
(𝑎0, 𝑎1, . . . , 𝑎𝑛−1)
𝐴 𝑥0𝐴(𝑡)(𝑥0)
𝑡 𝐴 𝑥0𝑡∈ {0,1, . . . , 𝑛 −1}

𝑏0, 𝑏1, . . . , 𝑏𝑛−1
𝐴(𝑥) =
𝑛−1
𝑗=0
𝑏𝑗(𝑥−𝑥0)𝑗,
𝐴(𝑡)(𝑥0)𝑡∈ {0,1, . . . , 𝑛 −1}
𝑂(𝑛)
𝑏𝑖𝑂(𝑛log 𝑛)
𝐴(𝑥0+𝜔𝑘
𝑛)𝑘∈ {0,1, . . . , 𝑛 −1}
𝐴(𝑥0+𝜔𝑘
𝑛) =
𝑛−1
𝑟=0
𝜔𝑘𝑟
𝑛
𝑟!
𝑛−1
𝑗=𝑟
𝑓(𝑗)𝑔(𝑗−𝑟)
,
𝑓(𝑗) = 𝑎𝑗𝑗!𝑔(𝑙) = 𝑥𝑙
0/(𝑙!)
𝐴(𝑥0+𝜔𝑘
𝑛)𝑘∈ {0,1, . . . , 𝑛−1}
𝑂(𝑛log 𝑛)