On the Polynomial Multiplication in Chebyshev Form


Akleylek S., Cenk M. , ÖZBUDAK F.

IEEE TRANSACTIONS ON COMPUTERS, vol.61, no.4, pp.584-587, 2012 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 4
  • Publication Date: 2012
  • Doi Number: 10.1109/tc.2011.38
  • Title of Journal : IEEE TRANSACTIONS ON COMPUTERS
  • Page Numbers: pp.584-587
  • Keywords: Chebyshev polynomials, theory of computation, multiplication of polynomials, arithmetic complexity., INTERPOLATION

Abstract

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.