A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition

• DOI: 10.1137/18m1180827
• Publication Date: 2019-01-30T18:52:07Z
• Authors: Thomas Y. Hou; De Huang; Ka Chun Lam; Ziyun Zhang
• Keywords: Matrix (chemical analysis); Multiresolution analysis; Operator (biology)

In this paper we propose a new iterative method to hierarchically compute relatively large number of leftmost eigenpairs sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit well-conditioned property every decomposition component by integrating framework into implicitly restarted Lanczos method. achieve combination proposing an extension-refinement scheme, in which intrinsic idea is decompose target spectrum several segments such that corresponding eigenproblem each segment well-conditioned. Theoretical analysis and numerical illustration are also reported illustrate efficiency effectiveness algorithm.