Approximate complex polynomial evaluation in near constant work per point
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Proof, Completeness, Transcendentals, and Sampling
Journal of the ACM (JACM)
Evaluating a polynomial and its reverse
ACM SIGACT News
On the complexities of multipoint evaluation and interpolation
Theoretical Computer Science
Matrix-vector multiplication in sub-quadratic time: (some preprocessing required)
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Computer and System Sciences
Improved twiddle access for fast fourier transforms
IEEE Transactions on Signal Processing
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A polynomial p(x) can be evaluated at several points x1,...,xm by first constructing a polynomial d(x) which has x1,...,xm as roots, then dividing p(x) by d(x), and finally evaluating the remainder r(x) at x1,...,xm. This method is useful if the coefficient sequence of d(x) can be chosen to be sparse, thus simplifying the construction of r(x). The case m&equil;1 and d(x) &equil; x−x1 is Horner's rule, while the case d(x) &equil; xm−1 yields the fast Fourier transform algorithm.