Optimization of Polynomial Approximation Algorithms for Sinusoidal Functions

• Main Authors: Yang-lung Chiu, 邱彥榕
• Other Authors: Tzong-yeu Leou
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/97642395055311217988

碩士 === 國立臺灣科技大學 === 電子工程系 === 97 === In this thesis, we have explored the optimization of polynomial approximation algorithm for sinusoidal function such that a polynomial function of suitable degree and the corresponding coefficients can be determined for a specific numerical processor to satisfied a predetermined error tolerance. The peak-constrained least-square (PCLS) algorithm is employed to compute the polynomial coefficients iteratively, where the relative weighting factor between the peak error and least-square error in the sinusoidal function approximation can be judiciously chosen. When the finite-precision effects of the polynomial coefficients are considered, the PCLS algorithm can be applied iteratively to find an appropriate set of polynomial coefficients in accordance to the order of significance of each coefficient. If the polynomial approximation is calculated with the Horner algorithm and the computation errors are to be considered, the polynomial coefficients can be further refined through the use of a local minimum search algorithm developed for the integer programming problem. The techniques proposed in this thesis have been verified with Matlab software simulation for 16-bit and 32-bit fixed-point processors, single-precision floating-point processor, double-precision floating- point processor, and the pertinent convergence properties and error character- istics of these techniques have been investigated. It is clearly seen that these polynomial approximation techniques can be applicable to various numerical processor and to a number of common functions suitable for polynomial approximation.