▍1. multiplication-table
只是一个课堂上做的九九乘法表,可能很多人做过(Just a class to do multiplication table, many people may have done)
只是一个课堂上做的九九乘法表,可能很多人做过(Just a class to do multiplication table, many people may have done)
其基本思想是取B样条函数 为及基函数,在[a,b]中均匀划分区间,xi=a+ih,h=(b-a)/n,由于三次样条函数空间是n+3维的,所以把分点扩充到x-1,xn+1,则任意三次样条函数可用 线性组合来表示:(The basic idea is to take B-spline function and basis functions in [a, b] in the evenly divided intervals, xi = a+ ih, h = (ba)/n, because the cubic spline function is n+3 dimensional space , so the expansion points to the x-1, xn+1, then any cubic spline function can be expressed as a linear combination:)
用C++来实现NEWTON迭代法解非线性方程算法数值分析,是数值分析里典型的一个算法。(In C++ to achieve NEWTON iterative numerical algorithm for solving nonlinear equations, numerical analysis is in a typical algorithm.)
单纯形法,求解线性规划问题的通用方法。单纯形是美国数学家G.B.丹齐克于1947年首先提出来的。它的理论根据是:线性规划问题的可行域是 n维向量空间Rn中的多面凸集,其最优值如果存在必在该凸集的某顶点处达到。顶点所对应的可行解称为基本可行解。单纯形法的基本思想是:先找出一个基本可行解,对它进行鉴别,看是否是最优解;若不是,则按照一定法则转换到另一改进的基本可行解,再鉴别;若仍不是,则再转换,按此重复进行。因基本可行解的个数有限,故经有限次转换必能得出问题的最优解。如果问题无最优解也可用此法判别。 (Simplex method for the minimum)
非常实用的时域仿真法暂态分析工具,利用牛顿法求解系统的微分方程组和代数方程组,得到转子摇摆曲线,判断暂态是否稳定(Very useful time-domain simulation tool for transient analysis method, using Newton method for solving systems of differential equations and algebraic equations, the rotor swing curves, to determine the stability of transient)
一个简单的网格生成程序,操作方便,易学,类似于easymesh!(A simple grid generation program, easy to operate, easy to learn, like easymesh!)
求解声学问题的边界元程序,给声学研究的人员很大启发(Solving the problem of acoustic boundary element program, to inspire great acoustic research staff)
在VS2005环境下,使用CUDA编程实现SAR成像中CSA算法的实现,得到了很好的加速比。(In the VS2005 environment, using the CUDA programming SAR imaging algorithm implementation in the CSA, has been very good speedup.)
涡格法计算机翼的涡强,对不同剖面形状,拱度等进行了比较分析。并且与书籍上对比(Vortex lattice method the computer wing of the vortex is strong, the shape of different profiles, such as camber, a comparative analysis.)
对于给定的一组轨迹点,用优化方法实现铰链四杆机构轨迹复演。优化方法为共轭梯度法。(For a set of track points,we use a optimization method to optimize the track of Hinge four-bar mechanism. The optimization method is conjugate gradient.)
编程序,按如下要求来求解n元一次线性方程组(假设方程组具有唯一解)。 (1)方程个数n之值由用户通过键盘输入; (2)方程组存放在“增广矩阵”A之中,而n行n+1列的A存储空间通过new来动态分配,且A的各元素值也由用户通过键盘输入 (Allocation procedures, the following requirements to solve the n-a system of linear equations (assuming a unique solution of equations). (1) the number n of the value equation by the user through the keyboard input (2) equations stored in the augmented matrix A, while n line n+ 1 column A storage space through the new dynamically allocated, and A The value of each element by the user through the keyboard input)
对于协方差矩阵的一种计算方法,对于地震中的反演约束算法能起到很好的作用。(For a kind of covariance matrix calculation method)
FFT快速傅里叶变换,用于数字信号处理,大大提高了运行速度,节省内存开销。C语言实现(FFT fast Fourier transform for digital signal processing, greatly improving the speed and save memory overhead. C language)
C + +程序,根据用户的输入可以产生特定的Gauss -1型切比雪夫正交规则,(C++ program which can generate a specific Gauss-Chebyshev type 1 quadrature rule, based on user input)
利用PHOTOSHOP软件可以量测出左右像片各控制点的像素坐标,通过公式可以计算出其像点坐标。再根据给定的控制点的空间坐标,利用直线线性变换解法计算出11个DLT参数即l的系数值以及内方位元素然后解算出外方位元素。另外一种方式是用单像空间后方交会的公式计算出外方位元素。利用单像空间后方交会的来结算影像的外方位元素的基本思想是:以单幅影像为基础,从该影像所覆盖地面范围内若干控制点的已知地面坐标和相应点的像坐标量测值出发,根据共线条件方程,解求该影像在航空摄影时刻的外方位元素。首先建立单文档的程序,建立一个对话框类,在这个类中进行像素坐标、控制点坐标文件的打开与读取,然后利用DLT公式进行外方位元素的解算。 数据检核部分用前方交会算法来进行,首先根据ID找到左右片的像点的同名点,然后计算变换矩阵及系数,根据给定的内方位元素,利用公式解算出像点的控制点坐标,然后和给定的控制点坐标相比较即可进行精度评定。 (PHOTOSHOP software can be measured using a photo of the control points around the pixel coordinates can be calculated by the formula sit out the image point Standard. According to the given coordinates of control points, the use of straight-line method to calculate the linear transformation of 11 DLT parameters that the coefficient l Value and calculate the orientation elements of exterior orientation elements and solutions. Another way is to use a single formula as the calculation of space resection Orientation elements out. Use as space resection alone to settle the image exterior orientation is the basic idea: to single video As the basis of images from the ground covered by a number of control points within the known ground coordinates and image coordinates of corresponding points in the measured values , The realities of collinearity equation, find the image in the time of aerial photography exterior orientation elements. First, the process to establish a single document)
说明: 研究舍入误差的例程,可以帮助初学计算方法的人。(Of rounding error in the routine that can help beginners who calculation.)
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: 数值分析中的chebyshev拟合程序,学习数值分析的同学可以参考参考(Numerical Analysis of chebyshev fit program, students study and numerical analysis can refer to reference)