最小二乘逼近

Keywords Closed convex cone;gradient projection method;Least-squares solution;Inverse matrix problem;Inverse eigenvalue problem;Matrix completion problem;Optimal approximation

Article From 湖南大学；应用数学博士论文 2005年度闭凸锥；投影梯度法；最小二乘解；矩阵反问题；矩阵逆特征值问题；矩阵完全化；最佳逼近

A projection method is used to smooth out start and end points of the ruling line sets. With predefined Euclidean 6 space distances, the problem of ruled surface approximation from line sets in Euclidean 3 space can be converted into a least square B-spline curve fitting issue in Euclidean 6 space.

利用"投影"光顺法对齐直母线段族首末端点，再通过定义欧氏6空间下的距离函数，将欧氏3空间下的直线族逼近直纹面问题转换成欧氏6空间下B样条曲线最小二乘拟合问题。

The method of least squares approximation for non-circular curve is suggested.

提出了一种利用最小二乘圆弧逼近非圆曲线的方法。

Commonly used algorithm c language, including some classic example, least squares, interpolation and approximation, etc.!

详细说明：常用算法的c语言实现，包括一些经典的比如，最小二乘，插值与逼近等等！

In order to calculation Lyapunov exponent spectrum of unknown system,firstly,reconstruct phase space of observed one-dimensional time series,secondly,use Least-Squared Support Vector Machine approximate dynamical equation of reconstruction system and calculation Lyapunov exponent spectrum by Jacobian matrix.

为了计算未知系统的Lyapunov指数谱，首先，对一维观测数据序列进行相空间重构，然后，利用最小二乘支持向量机逼近重构系统的动力学方程，再通过雅克比矩阵计算Lyapunov指数谱。

Keywords constrained matrix equation problem;sub matrix constraint problem; matrix norm; optimal approximation solution;least-squares solution

约束矩阵方程问题；子矩阵约束问题；矩阵范数；最佳逼近解；最小二乘解

These results are applied to solve a class of inverse eigenvalue problems for real matrices with a submatrix constraint and the expression of general solution and best approximation are also given.

最后，将所得的结果应用于子阵约束下实矩阵特征值反问题的最小二乘问题，得到了该问题解的表达式与最佳逼近解。

The deep knowledge repository of temperature profile was yielded based on the determinant mathematical model, which increased the 'extrapolative ability' and 'reliability'. Simulation results have proved that the model presented in this paper is simple, and can satisfy the control requirements.In order to predict and control, A real-time prognosticate model of temperature profile for a reverse flow reactor was built based on dynamic RBFNN with online correcting model parameters.

5基于改进的RBFNN的非线性内模控制策略充分利用神经网络的自学习及非线性逼近能力，建立流向变换反应器的动态模型和逆模型，非线性内模控制器由逆模型和带有一个调节参数的鲁棒滤波器组成，并采用递推最小二乘在线校正模型参数，仿真结果验证了此控制方案的有效性。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失