第三章研究了投影梯度方法的误差界估计。
In Chapter 3, some error bounds estimations of the projected gradient methods are obtained.
本文讨论了一类最简单的遍历马氏信源的误差界估计问题。
In this paper, the problem of the estimation of the error bound for a class of simplest Markov sources is discussed.
在误差界假设条件下，我们得到了改进算法的线性收敛速度。
Furthermore, by using an error bound condition, we establish linear convergence of the proposed algorithm.
借助于全局误差界的分析，证明了所提方法具有R -线性收敛速度。
By means of analysing the global error bound, we prove that the method has a R-linear convergence rate.
最后，通过这些误差界，我们给出了由投影梯度方法产生的迭代序列收敛的条件。
Using the error bounds, we give a condition for convergence of the sequence of iterates generated by projected gradient methods.
第一章是绪论部分。简要介绍了投影梯度方法，误差界估计以及本文的主要工作。
Chapter 1 is the introduction of this paper, which introduces the the projected gradient method, the error bounds estimation and the main results obtained in this paper.
最后给出了一个求解的下降法，并考察了最优化问题的误差界问题，以分析叠代法的收敛性。
Finally, wo present a descent method for solving VIP and study a global error bound for unconstrained optimization reformulation in order to discuss the convergence of itinerative method.
研究了矩阵列（行）一致扰动的几个性质，并应用于线性方程组。给出了线性方程组系数矩阵一致扰动下解的相对误差界。
Several properties about matrix with consistent perturbation are studied and applied into linear equations. Error bounds with the solution perturbation are given.
本文对矩量法的误差来源、误差界以及误差的主要作用范围进行了较全面的分析，并据此提出了若干提高准确度的改进措施。
In this paper the causes of errors, the error bounds and the action regions of errors in the moment method are analysized in detail. Some improvements on the accuracy of moment Solution are proposed.
证明了新的控制器一方面保证了运动的完全跟踪，另一方面保证了力跟踪误差是有界的且界的大小是可以调节的。
It is proven that the new controller can guarantee the perfect motion tracking. On the other hand, the force tracking error is bounded with the bound being adjustable.
证明了新的控制器一方面保证了运动的完全跟踪，另一方面保证了力跟踪误差是有界的且界的大小是可以调节的。
It is proven that the new controller can guarantee the perfect motion tracking. On the other hand, the force tracking error is bounded with the bound being adjustable.
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