• DocumentCode
    1421556
  • Title

    A Karatsuba-Based Algorithm for Polynomial Multiplication in Chebyshev Form

  • Author

    Lima, Juliano B. ; Panario, Daniel ; Wang, Qiang

  • Author_Institution
    Polytech. Sch. of Pernambuco, Univ. of Pernambuco, Recife, Brazil
  • Volume
    59
  • Issue
    6
  • fYear
    2010
  • fDate
    6/1/2010 12:00:00 AM
  • Firstpage
    835
  • Lastpage
    841
  • Abstract
    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
    Chebyshev approximation; computational complexity; interpolation; Chebyshev Form; Chebyshev coefficients; Karatsuba-based algorithm; interpolation techniques; polynomial multiplication; quadratic computational complexity; Algorithm design and analysis; Arithmetic; Chebyshev approximation; Circuit analysis; Computational complexity; Digital filters; Discrete cosine transforms; Interpolation; Polynomials; Roundoff errors; Senior members; Theory of computation; analysis of algorithms and problem complexity; computations on polynomials.;
  • fLanguage
    English
  • Journal_Title
    Computers, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9340
  • Type

    jour

  • DOI
    10.1109/TC.2010.45
  • Filename
    5416688