切比雪夫多项式零点插值与非线性方程求根

Solving Nonlinear Equation by Interpolation Based on Zero Point of Chebyshev Polynomial

基于切比雪夫正交多项式零点插值误差的极小化性质,提出了非线性方程求根的一种新方法.在此基础上建立迭代算法,进行误差估计,并通过数值试验对所建算法与弦截法、抛物线法进行收敛速度和精度的比较.

This paper proposes a new method for solving nonlinear equations by using minimization properties of interpolation error based on zero point of Chebyshev orthogonal polynomial.Based on this,a iteration algorithm is established and the error estimate is made.Then,by numerical experiments,the convergence speed and accuracy are compared between the proposed algorithm,the secant method and parabola method.