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引言斜量法亦名最速下降法,它是求解非线性和线性泛函方程[包括代数方程(组)、积分方程(组)等]的有效方法之一。目前国內的计算方法教科书上仅介绍了康托洛维奇最速下降法,其实,斜量法不止一种。例如,还有普通斜量法、弛缓法及赵访熊斜量法等几种,其中赵访熊斜量法是很值得推荐的一种。为简单起见,本文仅就解线性代数方程组的情形,介绍了赵访熊斜量法,分析了这种斜量法比起上面提到的其他三种斜量法的优点,还提到了推导这种斜量法的誤差估计式的一种方法,用与此类似的方法亦可导出其他三种斜量法的誤差估计式。§1.赵訪熊斜量法的簡单介紹
Introduction The oblique method, also known as the steepest descent method, is one of the effective methods for solving nonlinear and linear functional equations [including algebraic equations (groups), integral equations (groups), etc.]. At present, the calculation method textbooks in China only describe Cantolovich’s steepest descent method. In fact, there is more than one kind of oblique method. For example, there are several methods such as common oblique method, relaxation method, and Zhao visit bear oblique method. Among them, Zhao visit bear oblique method is very worthy of recommendation. For the sake of simplicity, this paper only introduces the method of solving the linear algebraic equations, and introduces the Zhao visit bear diagonal method. It analyzes the advantages of this oblique method over the other three oblique methods mentioned above, and also mentions the derivation. This method of estimating the error of the oblique method can also use the similar method to derive the error estimates of the other three methods. §1. Brief introduction of Zhao Chaoxiong oblique method