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% % time step https://ww2.mathworks.cn/matlabcentral/answers/184200-newton-raphson-loop-for-backward-euler % h = (t_final - t_init)/n; % with n number of time steps % % vectors % t = [tinit zeros(,n)]; % time % y = [yinit zeros(,n)]; % solution % % B…
在寻找极大极小值的过程中,有一个经典的算法叫做Newton's method,在学习Newton's method的过程中,会引入两个矩阵,使得理解的难度增大,下面就对这个问题进行描述. 1, Jacobian矩阵矩阵 对于一个向量函数F:$R_{n}$ -> $R{m}$是一个从欧式n维到欧式m维空间的函数(好像有点难理解,请看下面),这个函数由m个实函数组成,每一个函数的输入自变量是n维的向量,即$(y_{1}(x_{1},\cdots,x_{n}), \cdots,y_{m}(x_{1},…
 Newton Raphson Method: Advantages and Drawbacks:   v=QwyjgmqbR9s" target="_blank"> https://www.youtube.com/watch?v=QwyjgmqbR9s Advantages: converge fast, if it converges. requires only one guess. Secent method: you have to make 2 gues…
一.GBDT的通俗理解 提升方法采用的是加法模型和前向分步算法来解决分类和回归问题,而以决策树作为基函数的提升方法称为提升树(boosting tree).GBDT(Gradient Boosting Decision Tree)就是提升树算法的一种,它使用的基学习器是CART(分类和回归树),且是CART中的回归树. GBDT是一种迭代的决策树算法,通过多轮迭代,每轮学习都在上一轮训练的残差(用损失函数的负梯度来替代)基础上进行训练.在回归问题中,每轮迭代产生一棵CART回归树,迭代结束时将得…
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 ex…
Density Function The Generalized Gaussian density has the following form: where  (rho) is the "shape parameter". The density is plotted in the following figure: Matlab code used to generate this figure is available here: ggplot.m. Adding an arbi…
In the previous post, we talk about a very popular Boosting algorithm - Gradient Boosting Decision Tree. The key of GBM is using Gradient Descent to optimize the loss function. But why Gradient Descent, not other numeric optimization method? Is it th…
This is the second post in Boosting algorithm. In the previous post, we go through the earliest Boosting algorithm - AdaBoost, which is actually an approximation of exponential loss via additive stage-forward modelling. What if we want to choose othe…
OpenCASCADE解非线性方程组 eryar@163.com Abstract. 在科学技术领域里常常提出求解非线性方程组的问题,例如,用非线性函数拟合实验数据问题.非线性网络问题.几何上的曲线曲面求交问题等.OpenCASCADE中有关于非线性方程组定义的类及其求解类,本文主要介绍如何在OpenCASCADE中定义非线性方程组,及对其进行求解. Key Words. Function Set, Function Set Root, Newton Raphson Algorithm 1.In…
Apply Newton Method to Find Extrema in OPEN CASCADE eryar@163.com Abstract. In calculus, Newton’s method is used for finding the roots of a function. In optimization, Newton’s method is applied to find the roots of the derivative. OPEN CASCADE implem…