A SURVEY OF METHODS OF COMPUTING MINIMAX AND NEAR-MINIMAX POLYNOMIAL APPROXIMATIONS FOR FUNCTIONS OF A SINGLE INDEPENDENT VARIABLE
A SURVEY OF METHODS OF COMPUTING MINIMAX AND NEAR-MINIMAX POLYNOMIAL APPROXIMATIONS FOR FUNCTIONS OF A SINGLE INDEPENDENT VARIABLE
复制标题
DOI：
10.1145/321281.321282
复制
发表时间：
1965-01-01
影响因子：
2.5
通讯作者：
FRASER, W
中科院分区：
文献类型：
--
作者：
FRASER, W
描述了推导极小极大和近极小极大多项式逼近的方法。对于极小极大逼近，考虑了解析定义的函数和由值表定义的函数的技巧。对于近极小极大近似，首先描述了确定傅里叶-切比雪夫展开系数的方法。这包括重新排列幂多项式的系数，以及从定义它们的积分或定义函数的微分方程直接确定系数。最后，给出了一种方便的修正内插方法，该方法无需数值积分或方程组的数值解即可求出近似极小极大逼近系数。
Methods are described for the derivation of minimax and near-minimax polynomial approximations. For minimax approximations techniques are considered for both analytically defined functions and functions defined by a table of values. For near-minimax approximations methods of determining the coefficients of the Fourier-Chebyshev expansion are first described. These consist of the rearrangement of the coefficients of a power polynomial, and also direct determination of the coefficients from the integral which defines them, or the differential equation which defines the function. Finally there is given a convenient modification of an interpolation scheme which finds coefficients of a near-minimax approximation without requiring numerical integration or the numerical solution of a system of equations.