基于黄金分割的共轭梯度法步长求取方法  

Computation of the Step of Conjugate Gradient Method Based on Golden-section

作　　者：杜雄[1] 黄慧明[1] 杨艳[1] 

机构地区：[1]武汉大学物理科学与技术学院,武汉430072

出　　处：《科技通报》2016年第6期1-4,9,共5页Bulletin of Science and Technology

基　　金：国家科技重大专项课题(2011ZX05003-003)资助项目

摘　　要：目前在波形反演中常用梯度类算法的关键三要素为:目标函数、梯度和步长。在使用梯度类方法时,合适的步长因子可以有效地提高波形反演的计算效率和反演精度,故步长问题的研究也具有重要意义。基于PRP共轭梯度法进行波形反演,对现有的步长计算公式进行分析研究,提出了一种将经验步长公式与黄金分割法结合的步长计算方法,通过数值模拟试验,验证了采用的方法不仅能基本满足运算效率的要求,还能使反演结果更接近于目标模型。The three key factors for waveform inversion method based on gradient are objective function, gradient and step length. When using methods of gradient, proper step length factor can effectively improve the computation efficiency and inversion accuracy, so the research on step length is also of great significance. In this paper, we did research on defining the step base on the inversion problem with PRP conjugate gradient method, and introduced a new method to search the step length which was combined of the experience step formula with the golden-section method .The results of the numerical experiments showed that the method can not only basically meet the requirements of the efficiency, but also make the inversion results much closer to the real model.

关 键 词：黄金分割 共轭梯度法 步长 反演 

分 类 号：O411.3[理学—理论物理]