fortran_nr

说明：  所给的m文件中有详细的构造三对角分块矩阵的方法，而且构造的分块矩阵采用的是稀疏存储的方法，适用于大型三对角分块矩阵的构造(There are detailed methods to construct tridiagonal block matrix in the given m file, and the method of sparse storage is used to construct the block matrix, which is suitable for the construction of large tridiagonal block matrix.)

这是几篇关于粒计算在故障诊断中的应用，对学习粒计算的应用很有帮助。(This is a few on Granular Computing in Fault Diagnosis of learning the application of granular computing helpful.)

数学中的通径分析问题，主要用于数学实验方面，计算数学中的数据分析(Path analysis of mathematical problems in)

详细介绍了有限元法基础知识，对有限元入门者很有帮助(Details the basics of the finite element method, finite element beginners helpful)

共轭梯度法（Conjugate Gradient）是介于最速下降法与牛顿法之间的一个方法，它仅需利用一阶导数信息，但克服了最速下降法收敛慢的缺点，又避免了牛顿法需要存储和计算Hesse矩阵并求逆的缺点，共轭梯度法不仅是解决大型线性方程组最有用的方法之一，也是解大型非线性最优化最有效的算法之一(Conjugate gradient method (Conjugate Gradient) is between the steepest descent method and Newton' s method between a method that takes only a first derivative information, but to overcome the slow convergence of the steepest descent method shortcomings, but also avoid the need to store Newton and computing the inverse Hesse matrix and disadvantages, conjugate gradient method is not only to solve large linear equations of the most useful methods, large-scale nonlinear optimization solution is the most efficient algorithms)

本程序可模拟ND情况下的傅里叶变换，经过验证无误(This program can simulate the Fourier transform of the ND situation, and after the test, the program is correct )

％ 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)

说明：  解大规模线性方程组的预条件Gmres方法.系数矩阵可以非对称正定.(Solution of large-scale linear equations of the preconditioned GMRES method. Coefficient matrix can be non-symmetric positive definite.)

对于abaqus子程序学习的初学者，这是一个学习umat的很好算例,(Abaqus subroutine for beginners to learn, this is a good example to learn umat,)

最小二乘法求超定线性方程组得C＋＋模板，还包括矩阵求逆，矩阵乘法等小函数(Overdetermined least-squares method of linear equations have to C templates, also includes matrix inversion, matrix multiplication, such as small function)