非线性方程组求解

二阶非线性耦合波方程组的计算 The calculation of the second-order nonlinear coupled wave equations(The calculation of the second-order nonlinear coupled wave equations)

可以用于科学计算的库，数值计算库，只要将头文件包含即可。(Can be used for scientific computing libraries, numerical libraries, header files will be included as long as you can.)

首先根据高斯白噪声频率充满整个频带的特性，通过双树复小波包变换对高斯白噪声进行分解，利用频带能量泄漏的定量分析方法，验证了双树复小波包变换具有较低的频带能量泄漏特性；其次利用双树复小波包变换逐层分解信号，对每层分解所得分量求其FFT谱的峭度，得到基于双树复小波包变换的谱峭度图，根据图中峭度最大的原则，可以自动准确的选择信号分解最佳层数和最佳分量；最后将基于双树复小波包变换的谱峭度图的故障诊断方法应用于实际工程中，对齿轮故障振动信号进行分析，选择最佳分解层数和分量后利用希尔伯特包络解调，有效准确地提取了故障特征信息，验证了方法的可行性和有效性(The parameters of a filter were determined by experience, and that has a great influence on the results of signal processing. The discrete wavelet packet transform has a larger energy leakage of frequency band, which obviously affected the results of the envelope demodulation. It is necessary to have a method with a lower energy leakage of the frequency band before envelope demodulation. The dual tree complex wavelet packet transform (DT-CWPT) was a new signal processing method that had many good qualities. Because the energy leakage of the frequency band was smaller when the signal was decomposed by a dual tree complex wavelet packet transform, the dual tree complex wavelet packet transform was used to extract the fault feature information in the field of fault diagnosis. In this paper, first, according to the characteristics of Gaussian white noise, whose frequency was full of the whole frequency band, Gaussian white noise was decomposed by a dual-tree complex wavel)

说明：  经过优化的C代码实现的Gauss-Seidel 迭代算法(Optimized C code of the Gauss-Seidel iterative algorithm)

说明：  利用四阶龙格库塔求解微分方程，并给出方程实例。(The fourth order Runge Kutta is used to solve the differential equation and an example is given.)

说明：  matlab的adi方法求解偏微分方程，精确度较高(ADI method of MATLAB for solving partial differential equations)

计算典型相关算法，求出最大投影向量,以及最大投影向量对应的相关系数 (calculate canonical correlations, find the largest correlation coefficients)

泽尼克拟合算法，包括直角坐标系拟合和极坐标系的拟合，成熟代码，还请放心！(Zernike fitting algorithm, including fitting, fitting and polar coordinates Cartesian coordinates of the mature code, please rest assured!)

基于Biegler动态优化正交配置法（联立算法）的matlab 代码，由M.Cizniar，M. Fikar等编写(dynopt is a set of MATLAB functions for determination of optimal control trajectory by given description of the process, the cost to be minimised, subject to equality and inequality constraints, using orthogonal collocation on fi nite elements method.)

说明：  在matlab实现基于Schmidt的QR分解，共轭梯度法等(QR decomposition based on Schmidt in MATLAB)