EXPERIMENTS WITH CONJUGATE GRADIENT ALGORITHMS FOR HOMOTOPY CURVE TRACKING

作     者：Irani, Kashmira M. Kamat, Manohar P. Ribbens, Calvin J. Walker, Homer F. Watson, Layne T. 

作者机构：Virginia Polytech Inst & State Univ Dept Comp Sci Blacksburg VA 24061 USA Georgia Inst Technol Sch Aerosp Engn Atlanta GA 30332 USA Utah State Univ Dept Math & Stat Logan UT 84322 USA 

出 版 物：《SIAM JOURNAL ON OPTIMIZATION》 (工业与应用数学会最优化杂志)

年 卷 期：1991年第1卷第2期

页      面：222-251页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Department of Energy [DE-FG05-88ER25068, DE-FG02-86ER25018] National Aeronautics and Space Administration [NAG-l-1079, NAS1-18471-24] National Science Foundation [CTS-8913198, DMS-8800995] Air Force Office of Scientific Research [89-0497] School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia Department of Mathematics and Statistics, Utah State University, Logan, Utah Army [DAAL03-88-K] 

主　　题：globally convergent homotopy algorithm nonlinear equations preconditioned conjugate gradient homotopy curve tracking sparse matrix matrix splitting bordered matrix 

摘      要：There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig s preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.