On the Polynomial Multiplication in Chebyshev Form

Date

2012-04-01

Author

Akleylek, Sedat
Cenk, Murat
Özbudak, Ferruh

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We give an efficient multiplication method for polynomials in Chebyshev form. This multiplication method is different from the previous ones. Theoretically, we show that the number of multiplications is at least as good as Karatsuba-based algorithm. Moreover, using the proposed method, we improve the number of additions slightly. We remark that our method works efficiently for any N and it is easy to implement. To the best of our knowledge, the proposed method has the best multiplication and addition complexity for the N-term polynomial multiplication in Chebyshev form with 3 <= N <= 13.

Subject Keywords

Chebyshev polynomials, Theory of computation, Multiplication of polynomials, Arithmetic complexity

URI

https://hdl.handle.net/11511/32195

Journal

IEEE TRANSACTIONS ON COMPUTERS

DOI

https://doi.org/10.1109/tc.2011.38

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

S. Akleylek, M. Cenk, and F. Özbudak, “On the Polynomial Multiplication in Chebyshev Form,” IEEE TRANSACTIONS ON COMPUTERS, pp. 584–587, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32195.