矛盾方程

介绍了人眼波前像差的概念以及用Zernike多项式表示的人眼波像差函数，采用Householder变换对矛盾方程的广义增广矩阵进行正交三角化，导出求解拟合系数的算法。

The concept of human eye 's aberration and the mathematical function of wave-front aberration expressed by Zernike polynomial were introduced . The matrix of inconsistent equation group of the algorithm was orthogonalized and triangulated by Householder transformation , and the Zernike coefficients were given directly .

求解线性矛盾方程组的递推Householder变换法

A recursive householder transformation algorithm for solving linear over-determined equations

为了提高计算精度，采用QR分解（Householder变换法）来解矛盾方程。

In order to improve the calculate precision the QR-Householder Transform is adopted in solve the equation .

利用切比雪夫多项式使矛盾方程组系数矩阵正交化，利用Householder变换直接解矛盾方程组，尽可能降低病态条件数，提高了计算精度。

The coefficient matrix is orthogonalized by using polynomial and the overdetermined equations are solved by Householder transformation . The numerical ill-condition is decreased as low as possible , hence the operational accuracy is increased .

一个310000×160000线性矛盾方程组的求解问题

Solving a 310000 by 160000 linear overdetermined system of equations

线性矛盾方程组的最小二乘法解法&处理流化床实验数据

Least square solution of linear contradictory equation & handling experimental data on fluidized bed

采用最小二乘法求解矛盾方程组，可获得误差最小的唯一解。

A technique for sieving the overdetermined system is gived by utilizing least-square method and the u-nique solution with minimum-error is obtained .

对于标准加入法中的非线性矛盾方程组，经相减法处理后，再用非线性最小二乘法求解。

The nonlinear inconsistent equations set in standard addition method was handled by subtraction and was solved by using a nonlinear least square method .

在点云离散的基础上，采用最小二乘法求解矛盾方程的方法来求取空间导数，进而获得数值通量；

The spatial derivatives , which are used to estimate the inviscid flux , are directly approximated by using least square method to solve the inconsistent equations .

在使用递推最小二乘算法时，通常考虑的情况是训练样本所构成的方程组为矛盾方程组时该算法的收敛情况。

When using Recursive Least Square Algorithm , it is merely considered the case that the equations composed by the preceding k sample data are contradictory equations .

并用法方程法及共轭斜量法求解了一种属于矛盾方程的挥舞运动系数方程组，取得一致结果。

The equations of blade flap motion coefficients are a set of contradiction equations , and are calculated by means of the normal equation method and the conjugate gradient method .