再论约束最小二乘法

Exposition and argumentation on constrained least square method

本文介绍的约束最小二乘法如同经典的最小二乘法一样 ,也普遍适用于各种科学领域。然而 ,这一方法仅在“模型修正”一类论文的附录中出现过。鉴于约束最小二乘法在计算力学和工程问题中愈来愈重要的作用 ,本文将作者十多年前提出的这一方法稍加扩展 (如引入加权因子和讨论了自然权因子的应用等 )后 ,再做一系统的介绍 ,并随意设计了一个简单考例 ,证实了约束最小二乘法的有效性。

As with the least square method, the Constrained Least Square (CLS) method can be used in the various fields of science. However the CLS method, in the past, were published only in the Appendixes of some papers of model correction, thus many researchers and engineers are restricted in respect of understanding the CLS method. Because the CLS procedure plays more and more important part in the analysis of various engineering problems, the authors develop further the CLS method proposed 10 years ago and present again systematically the CLS method in this paper. The results of a simple example, that is designed arbitrarily, show that the CLS method is very efficient.