基于牛顿迭代法的改进预估

A New Predictor corrector Method Based on Newton Iterative Method

为提高迭代法的收敛速度,对非线性方程求根的迭代法,从积分形式方程角度,将经典的牛顿迭代法与两点高斯积分公式相结合,提出一种新的预估校正格式--高斯勒让德牛顿法(Gauss Legendre Newton Method,简称GN法),并证明该方法对单根至少三阶收敛,比同阶的Simpson牛顿法具有更高的效率指数.数值算例结果表明,与其他3种迭代法相比,该方法具有较快的收敛速度和较高的效率指数.高温光谱温度反演结果表明,该方法具有较高的精度和一定的应用价值.

A new predictor corrector scheme,named Gauss Legendre Newton method(GN method),is proposed by combining the classical Newton iterative method and two point Gauss integral formula to improve the convergence.It is proved that the new method converges to a single root at least third order and has higher efficiency index than Simpson Newton method.Numerical results show that the new method has faster convergence speed and higher efficiency index than the other three iterative methods.The temperature inversion results of high temperature spectrum show that the method has high accuracy and application value.