xiaoboquzao

(有源代码)数值分析作业,本文主要包括两个部分,第一部分是常微分方程(ODE)的三个实验题,第二部分是有关的拓展讨论,包括高阶常微分的求解和边值问题的求解(BVP).文中的算法和算例都是基于Matlab计算的.ODE问题从刚性(STIFFNESS)来看分为非刚性的问题和刚性的问题,刚性问题(如大系数的VDP方程)用通常的方法如ODE45来求解,效率会很低,用ODE15S等,则效率会高多了.而通常的非刚性问题,用ODE45来求解会有很好的效果.从阶次来看可以分为高阶微分方程和一阶常微分方程,高阶的微分方程一般可以化为状态空间(STATE SPACE)的低阶微分方程来求解.从微分方程的性态看来,主要是微分方程式一阶导系数大的时候,步长应该选得响应的小些.或者如果问题的性态不是太好估计的话,用较小的步长是比较好的,此外的话Adams多步法在小步长的时候效率比R-K(RUNGE-KUTTA)方法要好些,而精度也高些,但是稳定区间要小些.从初值和边值来看,也是显著的不同的.此外对于非线性常微分方程还有打靶法,胞映射方法等.而对于微分方程稳定性的研究,则诸如相平面图等也是不可缺少的工具.值得提出的是,除了用ode系类函数外,用simulink等等模块图来求解微分方程也是一种非常不错的方法,甚至是更有优势的方法(在应用的角度来说).((Source code) numerical analysis homework, this docment includes two parts, the first is ordinary differential equations (ODE) of the three examples, the second part is about the expansion of the discussion, including the higher-order ordinary differential & boundary value solution Problems (BVP). the text of the algorithm and numerical examples are based on the Matlab. ODE from the rigid (STIFFNESS) look into the issue of non-rigid and rigid problem, rigid problems (such as large coefficient VDP equation) such as using the always method ODE45 used to solve the problems , efficiency will be low, with ODE15S the other hand, many of the high efficiency. and the usual problem of non-rigid, there will be used to solve ODE45 very good results. Judging from the order can be for high-order differential equations and first-order ordinary differential equations, higher-order differential equations can be transformed into a general state space (STATE SPACE) used to solve the low-order different)

一些MATLAB练习用的小代码.均为M文件。全是本人学习时写的。有注释。绝对原创。(MATLAB exercises with some small code. Are M documents. Learning all the time I wrote. Annotated. Absolutely original.)

实现了区域合并的图像分割的经典方法，是Interactive Image Segmentation by Maximal Similarity based Region Merging 论文的源码，可以好好研究(Regional integration to achieve the classic method of image segmentation is the Interactive Image Segmentation by Maximal Similarity based Region Merging paper source, you can carefully study)

通过matlab编程实现的一个对公司员工的姓名、性别、年龄、职位、工作年数统计的一个程序，精炼，实用。(Matlab programming a company employee' s name, gender, age, position, the number of years a program statistics, refining, and practical.)

基于公交上下客的客流OD矩阵推算，与参考文献所推数据完全一致。代码完全独创，实用价值高。(Transit OD Matrix estimation based on Passenger boarding and alighting. )

matlab应用，一个小波变换的滤波实例应用。(matlab application, a wavelet transform filter example application.)

说明：  matlab codes for calculate the control action of the ststems and that shown in the systems.

说明：  用matlab实现的稀疏字典学习算法，可以用于图像去噪、图像分类、图像识别等(Sparse dictionary learning algorithm implemented by Matlab can be used for image denoising, image classification, image recognition and so on.)

二阶系统与传统的PID和模糊控制相比较，并用MATLAB编程，进行了仿真对比(Second-order system with the traditional PID and fuzzy control in comparison with MATLAB programming, simulation comparison)

Toolbox for biomedical signal processing