A karatsuba-based algorithm for polynomial multiplication in chebyshev form
In this paper, we present a new method for multiplying polynomials in Chebyshev form. Our approach has two steps. First, the well-known Karatsuba's algorithm is applied to polynomials constructed by using Chebyshev coefficients. Then, from the obtained result, extra arithmetic operations are used to write the final result in Chebyshev form. The proposed algorithm has a quadratic computational complexity. We also compare our method to other approaches.
|Keywords||Analysis of algorithms and problem complexity, Computations on polynomials, Theory of computation|
|Journal||IEEE Transactions on Computers|
Lima, J.B. (Juliano B.), Panario, D. (Daniel), & Wang, Q. (2010). A karatsuba-based algorithm for polynomial multiplication in chebyshev form. IEEE Transactions on Computers, 59(6), 835–841. doi:10.1109/TC.2010.45