BLOCK ALGORITHMS WITH AUGMENTED RAYLEIGH-RITZ PROJECTIONS FOR LARGE-SCALE EIGENPAIR COMPUTATION

作     者：Haoyang Liu Zaiwen Wen Chao Yang Yin Zhang 

作者机构：Beijing International Center for Mathematical ResearchPeking UniversityBeijing 100871China Computational Research DivisionLawrence Berkeley National LaboratoryBerkeleyCAUSA Department of Computational and Applied MathematicsRice UniversityHoustonUSA 

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

年 卷 期：2019年第37卷第6期

页      面：889-915页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：国家自然科学基金 by Beijing Academy of Artificial Intelligence(BAAI) Most of the computational results were obtained at the National Energy Research Scientific Computing Center (NERSC),which is supported by the Director,Office of Advanced Scientific Computing Research of the U.S.Department of Energy under contract number D 

主　　题：Extreme eigenpairs Augmented Rayleigh-Ritz projection 

摘      要：Most iterative algorithms for eigenpair computation consist of two main steps:a subspace update(SU)step that generates bases for approximate eigenspaces,followed by a Rayleigh-Ritz(RR)projection step that extracts approximate *** far the predominant methodology for the SU step is based on Krylov subspaces that builds orthonormal bases piece by piece in a sequential *** this work,we investigate block methods in the SU step that allow a higher level of concurrency than what is reachable by Krylov subspace *** achieve a competitive speed,we propose an augmented Rayleigh-Ritz(ARR)*** this ARR procedure with a set of polynomial accelerators,as well as utilizing a few other techniques such as continuation and deflation,we construet a block algorithm designed to reduce the number of RR steps and elevate concurrency in the SU *** computational experiments are conducted in C on a representative set of test problems to evaluate the performance of two variants of our *** results,obtained on a many-core computer without explicit code parallelization,show that when computing a relatively large number of eigenpairs,the performance of our algorithms is competitive with that of several state-of-the-art eigensolvers.