基于Gauss求积公式的Newton迭代法

利用Gauss数值积分公式构造牛顿迭代法的变形格式,得到牛顿迭代方法的三个新格式,并证明了它们的收敛阶都为3。通过matlab编程进行数值试验,结果表明三个新格式具有较好的收敛速度。它们丰富了非线性方程求根的方法,在理论上和应用上都有一定的价值。

The Newton's Method Based on the Gauss Quadrature Formula

This paper mainly employs Gauss numerical integral formulas to construct the deformation of Newton iterative method, therefore, we get the three new formats of the Newton iterative method and prove its convergence order is 3. With the numerical tests of matlab, it is shown that the three new formats, compared with the Newton iterative method, have better convergence speed, which to some extent enrich the method of location of root for nonlinear equations and prove the value of it both in theory and applicat...