/// Newton-Raphson method --Calculate square root. /// </summary> /// <param name="n">The square root of n.</param> /// <returns>Returns the square root of n.</returns> public static double Sqrt(double n){ doubl
本期对Newton–Raphson Method的收敛性进行一个深入讨论。 Newton–Raphson方法并不能总是保证收敛到精确解。首先,它假设方程中解的增量相对较小。随着迭代次数的增加,Δu逐渐变小,最终在精确解处接近零。然而,当雅可比矩阵变得奇异,或者矩阵 KT 的行列式为零时,这一假设就被违反了。在这种情况下,Δu变为无穷大,...
Newton-Raphson MethodChapters, CourseReview, MathematicsConcepts, BasicConcepts, AdvancedLaws, GasMatrix, BasicLeast, LinearTests, Section
当当前迭代接近解时,该方法表现出二次收敛性。 Fig. 1 非线性方程P(u)=f 的Newton-Raphson方法 设uexact是精确解,un和un+1是Newton–Raphson方法解的两个连续近似值。然后,当存在常数c>0满足 ,则该方法呈二次收敛。由于左手边是第(n+1)次迭代时的误差,右手边是第n次迭代时误差的平方,因此Newton–Raphson...
In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function. It is one example of a root-finding algorithm. ...
Newton-Raphson method This method is based on the Newton-Raphson general algorithm for the solution of a set of simultaneous non-linear equations. F(X) = 0, where F is a vector of functions f1 to fn in variables x1, to xn. At each iteration of this method, the non-linear problem is...
Newton’s Method 牛顿法则, 又叫Newton-Raphson method 牛顿迭代法则 大体就是不停的迭代,求近似值, 在点(x1, f(x1)) 做对应的切线 这个时候,如果和x轴的截点为(x2,0),则有: 当 的时候,可以得到: 同理,我们可以得到x3: 依次类推,可以不停的迭代下去 我们观察对应的图像: ...
polynomials/ C4150 Nonlinear and functional equations (numerical analysis)The only difficulty involved in the Newton-Raphson method is how to make the initial guess. This paper presents a two-transformation technique which enables us to make the initial guess unnecessary. Several characteristic equations...
Although this is the most basic non-linear solver, it is surprisingly powerful. It is based on the Newton-Raphson method in chapter 9.6-7 of Numerical Recipes in C. In general for well behaved functions and decent initial guesses, its convergence is at least quadratic. However it may fail ...
非线性方程组newton-raphson算法 牛顿-拉夫逊(Newton-Raphson)算法是一种多元非线性方程组求根的迭代式方法,俗称牛顿法或拉夫逊法,是尤为重要的数值计算和求根技术。 牛顿-拉夫逊算法以牛顿求根法和拉夫逊改进为基础,以多元非线性方程组的原型函数求解其解析解,并迭代式地求取解向量,从而使多元非线性方程组得以求解...