Polynomial-arithmetic-calculation

用来作为数学建的参考资料学习，希望对爱好则用所帮助(math model study study .Used as a reference material for Mathematical Studies)

说明：  有两个ARMA过程，其中信号1是宽带信号，信号2是窄带信号，分别用AR谱估计算法、ARMA谱估计算法和周期图法估计其功率谱。(There are two ARMA processes, in which signal 1 is a wideband signal and signal 2 is a narrowband signal. The power spectrum is estimated by AR spectrum estimation algorithm, ARMA spectrum estimation algorithm and periodogram method respectively.)

大型上用有限元软件ABAQUS的用户自定义材料子程序UMAT，用于计算材料低周疲劳极限和损伤下的应力应变关系(calculating material low cycle fatigue limit)

说明：  二分法求方程数值解，程序含说明性文字，精度可调(The numerical solution of the equation is obtained by dichotomy. The program contains explanatory text and the precision is adjustable)

打靶法求微分方程边值问题，这是数学上的求取方程问题的边值的方法 (Shooting method for boundary value problems for differential equations, which is to strike a mathematical equation of the boundary value problem approach)

采用离散的数值方法，通过坐标转换并生成贴体网格系统，计算轴对称喷管流场(Discrete numerical methods, through coordinate transformation and generate body-fitted grid system, calculating axisymmetric nozzle flow)

对于方程组AX=b，当系数矩阵非奇异时，对原方程进行改写，利用公式X^k=BX^(k+1)+g进行迭代求解。(For equations AX = b, when the coefficient matrix is ​ ​ nonsingular, rewriting the original equation, using the formula X ^ k = BX ^ (k+1)+g for iterative solution.)

最小二乘估值的SVD分解计算方法，本程序可将最小二乘估值问题转化为超定方程组的问题处理，且可用奇异值分解的方法计算最小二乘问题。(Least Squares Estimates of the SVD decomposition method, the valuation process can be transformed into squares overdetermined equations deal with the problem, and can be calculated singular value decomposition least squares problem.)

ABAQUS的二次开发，非常适合学习VDLOAD的同志们学习，来自廖公云老师的《ABAQUS有限元软件在道路工程中的应用》(Learning from Liao Gongyun teacher "ABAQUS finite element software ABAQUS secondary development, very for learning VDLOAD, comrades in road works")

ABAQUS中的循环模型umat，并附有解释，实现循环加载下的模拟(Cycle model in ABAQUS umat, along with explanation, to achieve the simulation under cyclic loading)