FEM

压缩包包含三个文件： 全主元高斯-约当消元法程序AGJDN.m；基于全主元高斯-约当消元法的迭代求解病态矩阵方法AGJDNM.m；AGJDN.m的测试方程。 程序参考自：Fortran常用算法程序集（第二版） 徐世良编。AGJDN.m能求解部分病态矩阵，而AGJDNM.m对于我的测试矩阵效果不佳，但也一并上传，仅供参考。 错漏之处，还望指正。 (Gaussian-Jordan elimination base on all principal element.)

FFT快速傅里叶变换 采用基4 fft实现的c语言版(FFT Fast Fourier Transform implemented using the base 4 fft c language version)

新建复数类进行复数运算，重载+、=+、*、/等运算符用于复数间的运算。(New complex class complex operation, overloading+ =+,*,/operator for computing the plural.)

％ 奇异值分解 (sigular value decomposition,SVD) 是另一种正交矩阵分解法；SVD是最可靠的分解法， ％ 但是它比QR 分解法要花上近十倍的计算时间。[U,S,V]=svd(A)，其中U和V代表二个相互正交矩阵， ％ 而S代表一对角矩阵。 和QR分解法相同者， 原矩阵A不必为正方矩阵。 ％ 使用SVD分解法的用途是解最小平方误差法和数据压缩。用svd分解法解线性方程组，在Quke2中就用这个来计算图形信息，性能相当的好。在计算线性方程组时，一些不能分解的矩阵或者严重病态矩阵的线性方程都能很好的得到解( Singular value decomposition (sigular value decomposition, SVD) is another orthogonal matrix decomposition method SVD decomposition is the most reliable method, but it takes more than QR decomposition near ten times the computing time. [U, S, V] = svd (A), in which U and V on behalf of two mutually orthogonal matrix, and the S on behalf of a diagonal matrix. And QR decomposition are the same, the original matrix A is no need for the square matrix. The use of SVD decomposition method are used as a solution of least squares error method and data compression. Using SVD decomposition solution of linear equations, in Quke2 on to use this information to calculate the graphics performance quite good. In the calculation of linear equations, some indecomposable matrix or serious pathological matrix of linear equations can be a very good solution)

进行主成分分析的多种方法，简单和复杂的，适合初学者使用(For a variety of methods of principal component analysis, simple and complex, suitable for beginners to use)

泽尼克多项式来表示波前形状，此程序运用matlab求得泽尼克多项式系数( Searched: Entire Web Site Advanced Search Results 1 through 9 of 9 Zernike Polynomial Coefficients for a given Wavefront using Matrix Inversion in Matlab )

共炮点地震波正演，其中、包括了直达波，反射波，折射波(Common shot point synthesis of reflected wave records)

用牛顿法，共轭梯度法，最速下降法完成矩阵的计算(Newton conjugate gradient method)

快速排序法和堆排序法Fortran90程序，其中快速排序法使用到了递归过程，因此对于堆栈要求较高(both Quicksort and Heapsort program are used for sort array. Note that a recursion process is used in Quicksort program, Thus it need require a relative high stack size.)

把 Maxwell 方程式在时间和空间领域上进行差分化。利用蛙跳式(Leap frog algorithm)--空间领域内的电场和磁场进行交替计算，通过时间领域上更新来模仿电磁场的变化，达到数值计算的目的。(The Maxwell equations in time and space on the field differencing. Using the leapfrog (Leap frog algorithm)- Space field for alternating electric and magnetic fields calculated by the time domain electromagnetic field is updated to mimic the changes to achieve the purpose of numerical calculation.)