Efficient Reduction Algorithms for Banded Symmetric Generalized Eigenproblems via Sequentially Semiseparable (SSS) Matrices

Fan Yuan, Shengguo Li, Hao Jiang, Hongxia Wang, Cheng Chen, Lei Du and Bo Yang
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Fan Yuan: College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China
Shengguo Li: College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China
Hao Jiang: College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China
Hongxia Wang: College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
Cheng Chen: Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
Lei Du: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
Bo Yang: College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China

Mathematics, 2022, vol. 10, issue 10, 1-13

Abstract: In this paper, a novel algorithm is proposed for reducing a banded symmetric generalized eigenvalue problem to a banded symmetric standard eigenvalue problem, based on the sequentially semiseparable (SSS) matrix techniques. It is the first time that the SSS matrix techniques are used in such eigenvalue problems. The newly proposed algorithm only requires linear storage cost and O ( n 2 ) computation cost for matrices with dimension n , and is also potentially good for parallelism. Some experiments have been performed by using Matlab, and the accuracy and stability of algorithm are verified.

Keywords: generalized eigenvalue problems; rank-structured matrix; SSS matrix; banded reduction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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