最小二乘问题

矩阵的Moore-Penrose逆和最小二乘问题的条件数

Condition Numbers for Moore-Penrose Inverse of Matrix and Linear Least Squares Problem

用Givens变换解最小二乘问题

Solving the Least Squares Problem with Givens Transformation

非线性最小二乘问题的结构p步牛顿法

Structured p step Newton Algorithm for Nonlinear Least Square Problems

解非线性最小二乘问题的结构化拟Newton方法是求解无约束最优化问题的标准拟Newton方法的推广。

The structured BFGS method is a quasi-Newton method for solving the nonlinear least squares problem .

标度整体最小二乘问题及对称代数Riccati方程的扰动分析及条件数

Perturbation Analysis and Condition Numbers of Scaled Total Least Squares Problems and Symmetric Algebraic Riccati Equations

用Householder变换解线性最小二乘问题的计算程序

An Algorithm for Linear Least squares solution by Householder Transform

讨论了整体最小二乘问题的解集与极小范数TLS解。

Solution sets and the minimun norn solution of the basic TLS problem are discussed .

2－块AOR迭代解最小二乘问题的最优收敛性

Optimal Convergence of Two-Block AOR Iteration for Solving Least Square Problems

用2-块AOR方法求解最小二乘问题的收敛域

Convergence Domains of a 2-Block AOR Method for Least-Squares Problems

随后二十多年的发展ABS算法扩展到可以求解最小二乘问题、不等式组、线性规划和具有线性约束的非线性规划等问题。

Throughout the following twenty years , ABS algorithms have been extended to solve the least squares , the inequality systems , linear programming and nonlinear programming with linear constraints etc.

在多视角测量数据融合中采用Screw理论，将坐标系关系求取中带约束的多变量非线性优化问题转化为线性方程组的最小二乘问题，简化了计算的复杂性，提高了求解过程的稳定性。

In coordinate computing , multiple variables non-linear optimized problems with constraint are changed into least squares problems of linear equation group utilizing screw theory , which simplifies the computing complexity and advanced stability in solving course .

将输出反馈极点配置问题转化为非线性最小二乘问题，用LM方法解出具有最小范数的反馈矩阵。

The output feedback pole assignment problem is transformed to a least square problem . The feedback matrix can be obtained by using LM algorithm .

在许多工程问题的应用中，会要求解整数最小二乘问题。LLL算法经常被作为一种预条件使用。

When solving the integer least squares problems arise in many engineering appli-cations , the LLL algorithm is widely used as a precondition .

本文考虑正则化的总体最小二乘问题（RTLS）。

In this paper , we consider the regularized total least square problems ( RTLS ) .

解等式约束非线性最小二乘问题的混合GN-BFGS方法

A hybrid gn-bfgs method for solving nonlinear least squares problem with equality constraints

肺磁场中弛豫曲线拟合的一个方法&非线性最小二乘问题的PSB算法

A method of relaxation curve fitting in the magnetic field produced by the lung & an algorithm of the Powell symmetric Broyden update for solving the nonlinear least-square problem

利用Volterra泛函级数描述非线性系统，将非线性系统辨识问题转化为标准的最小二乘问题，并通过QR分解进行求解。

By applying the Volterra series to describe the nonlinear system , the identification problem of nonlinear system is transformed into a normal least mean squares problem , which can be solved by QR decomposition .

文中对非线性最小二乘问题给出了一种新型求解方法&分块尺度化ABS求解方法，并证明了这类方法的局部超线性收敛性，最后在尺度矩阵取特殊值时给出了数值结果。

As a new type of method for nonlinear least square problems , the block scald ABS meth-ods are presented , and their locally superlinear convergence is proved . Finally the numerical re-sults are given with the special choice of the sealed matrices .

由于双基地声呐定位方程非线性的特点，应用求解非线性最小二乘问题的无约束最优化算法，给出了基于LMF方法的双基地声呐定位优化算法。

Third , based on the non-linearity feature of the system , the LMF algorithm is given by using the non-linearity least square optimal method .

文章就求解方程最为重要的Newton法以及解非线性最小二乘问题和解非光滑复合凸优化问题的Gauss-Newton法的收敛性等问题的研究成果和进展作介绍。

This survey is concerned with some recent results on convergence of the Newton method for solving nonlinear operator ( equation ) and the Gauss-Newton method for solving the least square problems and the convex composite optimization problems .

针对第二步中最小化重投影误差求出标定参数的最优解这个非线性最小二乘问题，提出了改进的LM法。

In the second step of these methods , a nonlinear least squares problem is proposed , whose aim is to find the optimal solution of the calibration parameters by minimize the reprojection error . An improved LM method is suggested .

该方法利用乘子罚函数把约束问题转化成解一系列一般的非线性最小二乘问题，并用Fletcher及Xu（1987）的混合GN-BFGS方法进行近似求解。

Multiplier penalty function is employed to transfer the problem into the solution of a series of general nonlinear least squares problems which are solved using the hybrid GN-BFGS method ( Fletcher and Xu , 1987 ) .

应用此法能细致地讨论约束条件与变量之间的关系，据此并可证明LSE问题与某一个无约束最小二乘问题的等价性。

By this method , the relationship between the constrained conditions and the variables can be discussed in detail , and thus it can be demonstrated the existance of an unconstrained least squares problem which is equivalent to LSE problem .

文中首先介绍了Givens变换的概念，叙述了用Givens变换解最小二乘问题的计算步骤，最后提供了更新未知参数及其协方差矩阵的算法。

This paper will first give the concept of Givens transformation , and then describe the computational procedure of solving the least squares prob-lim using Givens transformation , and finally deal with the algorithm of updating the parameter solutions and their covariance matrix .

理论上，利用Kronecker积，可以等价地将矩阵形式的约束最小二乘问题写成向量形式，因此，通解能够用高维空间的向量表示。

More and more people have been attracted in this research field . Theoretically , a least squares problem in matrix form can be rewritten in vector form by Kronecker product . So solutions of the matrix least squares problem are known in terms of higher dimensional column-vectors .

首先我们把欧氏距离模型转化为序列非负最小二乘问题，然后根据非负最小二乘问题的KKT条件转化为线性互补问题，基于线性互补问题我们提出了一种NMF算法。

First of all , we transform the Euclidean distance model into a sequence of least squares problems , from the non-negativity constrained least squares ' KKT conditions we have a linear complementarity problem ( LCP ), and then a new algorithm for NMF based on LCP is proposed .

对最小二乘问题的摄动定理的一点注记

A Note on the Perturbation Theorem of the Least Square Problem

广义非线性动态最小二乘问题的一个直接解算方法

A direct solution method for generalized nonlinear dynamic least squares problem

准确时序递归最小二乘问题的分块快速算法

The Efficient Algorithm for Block Implementation of Exact Recursive-Least-Squares Problems

解无约束优化及非线性最小二乘问题的自适应信赖域算法

Adaptive Trust Region Algorithms for Unconstrained Optimization and Nonlinear Least Squares Problems