numerical-analysis

系统仿真导论第一个实验程序，龙格库塔实验程序(Introduction The first experimental system simulation program, Runge-Kutta experimental procedures)

★问题描述: 给出平面上的N 个二维点，求出距离最小的2 个点对。本题中距离定义为他们的直 线距离。例如(0,0) (3,4)的距离为5. ★数据输入： 有多组数据，对于每组数据，第一行是一个数字N 表示点的个数。N=0 的时候说明 输入结束。之后N 行，每行有2 个浮点数x_i,y_i 表示第i 个点的坐标。(1<=N<=10000 0,0<=|x_i|,|y_i|<=10^9) ★结果输出: 输出一个浮点数，表示最近点对的距离除以2，保留2 位小数(四舍五入)。

假设有一个能装入总体积为T的背包和n件体积分别为w1 , w2 , … , wn 的物品，能否从n件物品中挑选若干件恰好装满背包，即使w1 +w2 + … + wn=T，要求找出所有满足上述条件的解。例如：当T=10，各件物品的体积{1，8，4，3，5，2}时，可找到下列4组解：（1，4，3，2），（1，4，5），（8，2），（3，5，2）。 [需求分析](Suppose there are a load of the backpack of the total volume of T and n volumes were w1, w2, ... wn items, whether selected from n items a number of exactly filled backpack, even if w1+w2+ ...+ wn = T, find out the solution of all the above conditions are met. For example: when T = 10, the volume of items {1,8,4,3,5,2}, can be found in the following four solutions: (1,4,3,2), (1,4,5 ), (8,2), (3,5,2). [Needs Analysis])

说明：  数值分析实验1.明确插值多项式和分段插值多项式各自的优缺点； 编程实现拉格朗日插值算法，分析实验结果体会高次插值产生的龙格现象；(Experiments of numerical analysis 1. Define the advantages and disadvantages of interpolation polynomials and piecewise interpolation polynomials. The Lagrange interpolation algorithm is programmed, and the Runge phenomenon produced by high-order interpolation is analyzed.)

Fluent 学习文件 全方位的指导手册 (Building geometry Setting boundary condition types)

说明：  复杂网络MATLAB工具包和源程序，用于计算复杂网络特性的工具包。(Complex network MATLAB toolkit and source code)

计算数码照片植被覆盖度。包括照片裁剪，RGB2HSL和计算(compute the vegetaion cover of digital image.)

本代码为《最优化理论与方法》书籍重的信赖域算法的代码，本代码中的目标函数和约束等初值可由需要进行改变，来得到所期望的计算(The code for the " optimization theory and method" heavy books trust region algorithm code, the code of the objective function and constraints may need to change the initial value to get the desired calculation)

二元二次多项式曲面拟合法的Matlab实现，含有M文件及数据文件示例(Binary quadratic polynomial surface fitting Matlab, contain the M-file and the data file example)

共轭梯度法（Conjugate Gradient）是介于最速下降法与牛顿法之间的一个方法，它仅需利用一阶导数信息，但克服了最速下降法收敛慢的缺点，又避免了牛顿法需要存储和计算Hesse矩阵并求逆的缺点，共轭梯度法不仅是解决大型线性方程组最有用的方法之一，也是解大型非线性最优化最有效的算法之一(Conjugate gradient method (Conjugate Gradient) is between the steepest descent method and Newton' s method between a method that takes only a first derivative information, but to overcome the slow convergence of the steepest descent method shortcomings, but also avoid the need to store Newton and computing the inverse Hesse matrix and disadvantages, conjugate gradient method is not only to solve large linear equations of the most useful methods, large-scale nonlinear optimization solution is the most efficient algorithms)