解超定病态线性方程组问题

给出超定方程组 Ax=b (1.1)其中A是秩为r的m×n矩阵,b是m维向量,x是n维未知向量. 目前处理病态线性方程组的方法大体上可以分为两类.一类是投影法(即降维法);另一类是正则化法.降维法是把右端向量b投影到A的极大线性无关列所张成的子空间中求解.数值相关性理论为其实际运用奠定了基础.降维法解病态线性方程组的     

AN ITERATED-SUBSPACE MINIMIZATION METHODS WITH SYMMETRIC RANK-ONE UPDATING

We consider an Iterated-Subspace Minimization(ISM) method for solving large-scale unconstrained minimization problems.At each major iteration of the method, a two-dimensional manifold, the iterated subspace, is constructed and an approximate minimizer of the objective function in this manifold then determined, and a symmetric rank-one updating is used to solve the inner minimization problem.     

一种求解离散多目标决策的心理学模型

本从心理学的角度，提出了一种基于后悔值的求解离散多目标决策问题的MPTBRV法，中还给出了相应的解法。     

A RESTARTING DIRECTION FOR THE CONJUGATE GRADIENT METHOD

The main purpose of this paper is to provide a restarting direction for improving on the standard conjugate gradient method.If a drastic non-quadratic behaviour of the objective function is observed in the neighbour of xk,then a restart should be done.The scaling symmetric rank-one update with Davidon's optimal criterion is applied to generate the restarting direction.It is proved that the conjugate gradient method with this strategy retains the quadratic termination.Numerical experiments show that it is successful.     

一个求解无约束优化问题的条件预优共轭梯度法

1 引言 考虑无约束最优化问题minf(x)(1.1)     

无约束极小化的自适应多信息下降法

对问题(1.1)已经提出了许多行之有效的计算方法,多信息方向法即是其中之一。1969年Miele-Cantrell提出了双信息梯度法。同年,在此基础上作为一个推广,Cragg-Levy又提出了多信息梯度法,并指出对干二次目标函数Miele-Cantrell方法等价于F—R共轭斜量法。其后在1975年M.A.Wolfe提出了更为有效的双信息拟牛顿法,1976年M.A.Wolfe和C.Viazmmsky合作对多信息方向法进行了归纳。这类算法的一般步骤是:     

A CHARACTERIZATION OF SELF-SCALING RANK ONE UPDATE

An analysis on the property of Self-Scaling Rank One Update (SSR1) is given. In view of it, we explore whether the SSR1 update without using exact line search possesses the finite termination property when it is applied to minimize a positive definite quadratic objective function.