Show how to apply the fast Fourier Transform to multiply three polynomials A(x) = a0 +a1x+a2x 2 +· · ·+an−1x n−1 of degree n−1, B(x) = b0 +b1x+b2x 2 +· · ·+bn−1x n−1 of degree n − 1, and C(x) = c0 + c1x + c2x 2 + · · · + cn−1x n−1 of degree n − 1 when n is a power of 2. Analyze its time complexity.
First multiply two polynomials using FFT, then multiply the result by the third polynomial.
The Time complexity will be nlog(n).
Use the following algorithm:
Algorithm 1. Add n higher-order zero coefficients to A(x) and B(x) 2. Evaluate A(x) and B(x) using FFT for 2n points 3. Pointwise multiplication of point-value forms 4. Interpolate C(x) using FFT to compute inverse DFT
Show how to apply the fast Fourier Transform to multiply three polynomials A(x) = a0 +a1x+a2x...
assume f(x)=a0+a1x+a2x^2+a3x^3+a4x^4... dont used this solution method pls because this not what the teacher want 4 Power Series Solutions to two important ODES 1. Find a power series (with two arbitrary constants) satisfying the following ODE S"(x) + f(2)=0 Write your answer in a closed form. 10 points Let f(2)= { an en f(x) non-don 22 on Žnin-Danza 3 anz":o. = { [ conta) (nt. Dants & an] 2n=o. (nta) (n+ Dant, tano. - (+) (0+2) (I+D (172) f(2)= {...