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

• 来源期刊: 计算数学（英文版）
• 关键词: Extreme eigenpairs Augmented Rayleigh-Ritz projection
• 年，卷（期）: 2019,（6）
• 页码范围: 889-915
• 页数: 27页
• 语种: 英文
• DOI: 10.4208/jcm.1910-m2019-0034

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 eigenpairs.So far the predominant methodology for the SU step is based on Krylov subspaces that builds orthonormal bases piece by piece in a sequential manner.In this work,we investigate block methods in the SU step that allow a higher level of concurrency than what is reachable by Krylov subspace methods.To achieve a competitive speed,we propose an augmented Rayleigh-Ritz (ARR) procedure.Combining this ARR procedure with a set of polynomial accelerators,as well as utilizing a few other techniques such as continuation and deflation,we construct a block algorithm designed to reduce the number of RR steps and elevate concurrency in the SU steps.Extensive computational experiments are conducted in C on a representative set of test problems to evaluate the performance of two variants of our algorithm.Numerical 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.