GreyRelation

实现复数运算符的重载，对C++初学者来说有一定的参考价值。(Complex operator overloading, C++ beginners a certain reference value . )

三次样条插值（简称Spline插值）是通过一系列形值点的一条光滑曲线，数学上通过求解三弯矩方程组得出曲线函数组的过程。本函数中采用第一类边界值(Cubic spline interpolation (referred Spline interpolation) through a series of key points of a smooth curve, mathematically by solving the three-moment equations derived curve function group process. This function uses the first boundary value)

采用动量梯度下降算法训练BP网络，采用两种训练方法，即 L-M 优化算法（trainlm）和贝叶斯正则化算法（trainbr），用以训练 BP 网络(Gradient descent algorithm using momentum BP network training, using two training methods, namely, LM optimization algorithm (trainlm) and Bayesian regularization algorithm (trainbr), to facilitate the training of BP network)

最速下降法就是梯度下降法,可以用于求解最小二乘问题(线性和非线性都可以)。可以说是求解机器算法的最古老、最经典的模型，另一种常用的方法是最小二乘法。(The steepest descent method is the gradient descent method, which can be used to solve the least squares problem (both linear and non-linear). It can be said that it is the oldest and most classical model for solving machine algorithm. Another commonly used method is the least square method.)

ABAQUS 显式计算时 用户自定义子材料程序 VUMAT源代码，(User defined subrutine of ABAQUS explicit analysis)

说明：  龙格-库塔方法的使用，例子 求y’=y-2x/y，y(0)=0。 解：输入X0=0，X1=1，H=0.2，N=6。()

J2流动理论加上破坏失效判据的程序，用于ABAQUS中的vumat程序，功能模拟加载到失效破坏的过程(J2 flow theory coupled with damage failure criteria of the program for the vumat ABAQUS program, functional simulation load to failure of the process of destruction)

说明：  这是数值分析的一些作业实验，文件中有详细的文档对理论，实验和算法的说明，用于病态方程组求解的源代码(This is the numerical analysis of the experimental operation, the paper detailed documentation of theory, experiment and the algorithm shows that morbid equation for solving the source code)

thermal damage abaqus-umat subroutine

经典矩阵运算问题求解(classic problem solving matrix operations)