Fast evaluation and interpolation
نویسنده
چکیده
A method for dividing a polynomial of degree (2n-l) by a precomputed nth degree polynomial in 0(n log n) arithmetic operations is given. This is used to prove that the evaluation of an nth degree polynomial at n+1 arbitrary points can be done in 0(n log^ n) arithmetic operations, and consequently, its dual problem, interpolation of an nth degree polynomial from 2 n+1 arbitrary points can be performed in 0(n log n) arithmetic operations. The best previously known algorithms required 0(n log^ n) arithmetic operations .
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