求解非线性算子方程的一类迭代法
A class of iterative methods for solving nonlinear operator equations
摘要：
本文讨论了Hilbert空间和巴拿赫空间上求解非线性算子方程的类梯度迭代法。作者制定了研究这种方法的一般原则。这一原则允许制定简单的条件下考虑的方法的收敛性，估计这种收敛的速度，并给出有效的先验和后验误差估计的标量函数的基础上构造的可逆性和光滑性的线性化的左手边的方程的估计。该原理适用于最小残数法、最速下降法最速下降法、最小误差法等经典方法的分析。主要结果是关于希尔伯特空间和巴拿赫空间上的算子方程具有一个特殊性质，即Bynum性质.
英文摘要：
The article deals with gradient-like iterative methods for solving nonlinear operator equations on Hilbert and Banach spaces. The authors formulate a general principle of studying such methods. This principle allows to formulate simple conditions of convergence of the method under consideration, to estimate the rate of this convergence and to give effective a priori and aposteriori error estimates in terms of a scalar function that is constructed on the base of estimates for properties of invertibility and smoothness of linearizations of the left-hand side of the equations under study. The principle is applicable for analysis of such classical methods as method of minimal residuals, method of steepest descent, method of minimal errors and others. The main results are obtained for operator equations on Hilbert spaces and Banach spaces with a special property, that is called Bynum property.
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