共查询到20条相似文献，搜索用时 46 毫秒
1.
张芳馨;郑仟;李登峰 《数学的实践与认识》2024,(5):190-197
考虑实l2上相位恢复问题.首先给出实l2上相位恢复的条件,包括充分条件、必要条件及充要条件;其次讨论实l2上范数恢复问题及实l2上有限个投影恢复问题,也给出与框架相关的范数恢复结论. 相似文献
2.
3.
解非线性最小二乘问题的锥模型算法 总被引：1，自引：1，他引：0
在自然科学研究、经济、统计等领域,非线性最小二乘有着广泛的应用,因而寻找快捷有效的算法有着十分重要的意义。它首先是一个最优化问题,同时又有自身的结构特点,充分利用其结构特点,是寻找更有效算法的关键。 相似文献
4.
加权广义逆、加权最小二乘和约束最小二乘问题 总被引：7，自引：0，他引：7
本文采用如下记号:记C~m×n是具有复数域的m×n长方矩阵的集合,C~m=C~m×1是m维向量的集合.对A∈C~m×n称A~H∈C~m×n是A的共轭转置矩阵,rank(A)表示A的秩,R(A)和N(A)分别为A的值域和零空间,||·||=||·||2和||·||F分别为2-范数和Frobenius范数;I表示恒等矩阵.人们在研究数学规划、数值分析、数据处理,散射理论和电磁学等领域中都将问题归纳为如下的最小二乘问题: 相似文献
5.
解非线性最小二乘问题的锥模型算法的局部收敛性 总被引：1，自引：0，他引：1
1 引言 对于非线性最小二乘问题 minf(x)=(1/2)sum from x=1 to m (r_i(x))~2=(1/2)R(x)~TR(x), (1.1)其中R(x)=(r_1(x),…,r_m(x))~T:DR~n→R~m,m≥n,有 g(x)=f'(x)=J(x)~TR(x), (1.2) H(x)=f(x)=J(x)~TJ(x)+sum from x=1 to m r_i(x)r_i(x), (1.3)其中J(x)=((r_i(x))/x_j)·Gauss-Newton方法,及Dennis等的改进方法,都是采用二次模型 相似文献
6.
7.
8.
9.
程毛林 《数学的实践与认识》2009,39(9)
对非线性回归模型进行非线性最小二乘估计一般需要确定参数初始值.在非线性回归模型中,General Logistic模型和Von Bertalanffy模型是二个含有四参数的增长曲线模型,对数据的拟合有较强的适应性,应用较为广泛.本文给出这两个模型参数初始值的确定方法,并应用于实际拟合,得到很好的效果. 相似文献
10.
11.
12.
Alternating least squares (ALS) is often considered the workhorse algorithm for computing the rank‐R canonical tensor approximation, but for certain problems, its convergence can be very slow. The nonlinear conjugate gradient (NCG) method was recently proposed as an alternative to ALS, but the results indicated that NCG is usually not faster than ALS. To improve the convergence speed of NCG, we consider a nonlinearly preconditioned NCG (PNCG) algorithm for computing the rank‐R canonical tensor decomposition. Our approach uses ALS as a nonlinear preconditioner in the NCG algorithm. Alternatively, NCG can be viewed as an acceleration process for ALS. We demonstrate numerically that the convergence acceleration mechanism in PNCG often leads to important pay‐offs for difficult tensor decomposition problems, with convergence that is significantly faster and more robust than for the stand‐alone NCG or ALS algorithms. We consider several approaches for incorporating the nonlinear preconditioner into the NCG algorithm that have been described in the literature previously and have met with success in certain application areas. However, it appears that the nonlinearly PNCG approach has received relatively little attention in the broader community and remains underexplored both theoretically and experimentally. Thus, this paper serves several additional functions, by providing in one place a concise overview of several PNCG variants and their properties that have only been described in a few places scattered throughout the literature, by systematically comparing the performance of these PNCG variants for the tensor decomposition problem, and by drawing further attention to the usefulness of nonlinearly PNCG as a general tool. In addition, we briefly discuss the convergence of the PNCG algorithm. In particular, we obtain a new convergence result for one of the PNCG variants under suitable conditions, building on known convergence results for non‐preconditioned NCG. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
13.
确定Lotka-Volterra生态系统模型高精度参数的研究 总被引：1，自引：0，他引：1
研究确定Lotka-Volterra生态系统模型的高精度参数估计问题.利用周期性,先对测量数据进行预处理;然后用三种不同的方法构造了误差函数,进行非线性最小二乘法参数估计;再用计算机仿真对其进行验证.结果表明该方法能够有效地解决高精度参数估计中消除测量数据误差的问题. 相似文献
14.
非线性回归方法的应用与比较 总被引：5，自引：0，他引：5
比较了非线性回归3种方法的数学原理:曲线直线化方法、非线性最小二乘方法、近似非线性法.说明了用方差分析确定回归模型的统计学意义、用决定系数R2描述曲线的拟合效果的理论依据.通过对同一问题用3种方法分析得出结论:非线性回归与近似非线性拟合方法决定系数相近(0.9966与0.9965),而曲线直线化决定系数为0.9738.因为近似非线性拟合方法无需选初值.建议应用近似非线性拟合方法. 相似文献
15.
Meng Huang & Zhiqiang Xu 《计算数学(英文版)》2020,38(4):638-660
We consider the rank minimization problem from quadratic measurements, i.e., recovering a rank $r$ matrix $X in mathbb{R}^{n×r}$ from $m$ scalar measurements $y_i=a_i^T XX^T a_i,;a_iin mathbb{R}^n,;i=1,ldots,m$. Such problem arises in a variety of applications such as quadratic regression and quantum state tomography. We present a novel algorithm, which is termed $exponential-type$ $gradient$ $descent$ $algorithm$, to minimize a non-convex objective function $f(U)=frac{1}{4m}sum_{i=1}^m(y_i-a_i^T UU^T a_i)^2$. This algorithm starts with a careful initialization, and then refines this initial guess by iteratively applying exponential-type gradient descent. Particularly, we can obtain a good initial guess of $X$ as long as the number of Gaussian random measurements is $O(nr)$, and our iteration algorithm can converge linearly to the true $X$ (up to an orthogonal matrix) with $m=Oleft(nrlog (cr)right)$ Gaussian random measurements. 相似文献
16.
林卫东 《纯粹数学与应用数学》1995,11(1):104-108
本文对具有状态终端约束、控制受限的非线性连续最优控制问题给出一种新的可实现的离散方法，此方法通过求解非线最小二乘问题避免这类问题离散后出现的不可行现象，文中给出这种做法的理论证明和实现方案。 相似文献
17.
基于最小二乘法的道路交通事故预测机理模型 总被引：1，自引：0，他引：1
基于相似理论提出一种新的道路交通事故预测方法,建立了新的交通事故预测非线性机理模型,作为道路交通事故预测的初步探讨.采用机动车保有量作为模型的输入变量,非线性最小二乘法求出模型参数.通过计算表明新预测模型预测精度较高,有应用价值,同时也为交通事故预测提出了新的预测理论. 相似文献
18.
就关节式机械臂指尖在任意两点间移动、沿固定曲线移动、机械臂绕开障碍物执行任务以及参数优化等问题展开研究.首先确定了自由度组合到指尖空间位置的映射,建立了求解上述问题的最小二乘模型、泛函条件极值模型,并给出了数值解法.最后,结合图像处理等技术,对各参数的优化设计提出了改进措施. 相似文献
19.
The nonnegative tensor (matrix) factorization finds more and more applications in various disciplines including machine learning, data mining, and blind source separation, etc. In computation, the optimization problem involved is solved by alternatively minimizing one factor while the others are fixed. To solve the subproblem efficiently, we first exploit a variable regularization term which makes the subproblem far from ill-condition. Second, an augmented Lagrangian alternating direction method is employed to solve this convex and well-conditioned regularized subproblem, and two accelerating skills are also implemented. Some preliminary numerical experiments are performed to show the improvements of the new method. 相似文献
20.
分布函数的非参数最小二乘估计 总被引：1，自引：0，他引：1
By using the non-parametric least square method, the strong consistent estimations of distribution function and failure function are established, where the distribution function F(x)after logist transformation is assumed to be approximated by a polynomial. The performance of simulation shows that the estimations are highly satisfactory. 相似文献