Today’s topic was the FFT. We didn’t get all the way through it, but Prof. Rudich will finish up on Monday. We started with definitions and assumptions about the ring we work with, but as a running example we used the simple ring Z_11. The key points of the FFT are that if we convert between coefficients and the sample point representation of a polynomial, we can compute the convolution by performing a linear number of multiplications.
The bulk of the lecture dealt with which sample points should we use: the nth roots of unity. They have some really nice properties that make the FFT work in sub-quadratic time.
We’ll finish discussing the matrix of the roots and its inverse on Monday. Please try to review the lecture in Kozen and bring some good questions to lecture.
Have a great weekend!