Title :
Algorithmic truncation of minimax polynomial coefficients
Author :
Tawfik, Sherif A. ; Fahmy, Hossam A H
Author_Institution :
Fac. of Eng., Cairo Univ., Giza
Abstract :
Elementary and high-level functions can be computed in hardware using polynomial approximation techniques. There are many techniques in the literature to calculate the coefficients of such polynomials. Remez algorithm as presented by Veidinger (1960) provides the optimal polynomial in the Chebyshev sense that is minimizing the maximum error (minimax approximation). This paper presents an algorithm for truncating the coefficients of the minimax polynomials obtained from Remez algorithm using an algorithmic method. A gain of 3 and 4 bits of accuracy over the direct rounding is reported. Muller addressed the same problem but his algorithm is applicable for the second order polynomials only. This paper presents an algorithm that is applicable for any order
Keywords :
Chebyshev approximation; minimax techniques; polynomial approximation; Chebyshev sense; MiniMax polynomial coefficients; Remez algorithm; algorithmic truncation; elementary functions; high-level functions; minimax approximation; optimal polynomial; polynomial approximation techniques; second order polynomials; Algorithm design and analysis; Approximation algorithms; Chebyshev approximation; Cost function; Equations; Hardware; Iterative algorithms; Minimax techniques; Mixed integer linear programming; Polynomials;
Conference_Titel :
Circuits and Systems, 2006. ISCAS 2006. Proceedings. 2006 IEEE International Symposium on
Conference_Location :
Island of Kos
Print_ISBN :
0-7803-9389-9
DOI :
10.1109/ISCAS.2006.1693111
