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Convolutions, Fast Fourier Transform and polynomials (2022)

Engineer

Before answering the question if we can do better than $O(n^2)$ to multiply polynomials, let's introduce the concept of convolution, since it will come in handy to understand what’s next. It may seem like a lot of operations, but for large polynomials this is way faster than the naive method that you were taught in high school. Adding all together, we can multiply polynomials in frequency domain in $O(nlogn)$ which is faster than what you were taught in high school.

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