A DIRECT SEARCH FRAME-BASED CONJUGATE GRADIENTS METHOD

作     者：I.D.Coope C.J.Price 

作者机构：DepartmentofMathematicsandStatisticsUniversityofCanterburyPrivateBag4800ChristchurchNewZealand 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2004年第22卷第4期

页      面：489-500页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Conjugate gradients Derivative-free Frame-based methods Numerical results 

摘      要：A derivative-free frame-based conjugate gradients algorithm is presented. Convergence is shown for C^1 functions, and this is verified in numerical trials. The algorithm is tested on a variety of low dimensional problems, some of which are ill-conditioned, and is also tested on problems of high dimension. Numerical results show that the algorithm is effective on both classes of problems. The results are compared with those from a discrete quasiNewton method, showing that the conjugate gradients algorithm is competitive. The algorithm exhibits the conjugate gradients speed-up on problems for which the Hessian at the solution has repeated or clustered eigenvalues. The algorithm is easily parallelizable.