Multiple-rank Modification of Symmetric Eigenvalue Problem

2017/06/02 by HyungSeon Oh, Zhe Hu, Oh, HyungSeon +1
Medicine · #FOS: Mathematics #Lymphoma Diagnosis and Treatment #Numerical Analysis (math.NA) #Viral-associated cancers and disorders

paper · pdf · doi:10.48550/arxiv.1706.00773

openalex publication_date 2017/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Rank-1 modifications in k-times (k > 1) often are performed to achieve rank-k modification. We propose a rank- k modification for enhancing computational efficiency. As the first step towards a rank- k modification, an algorithm to perform rank-2 modification is proposed and tested. The computation cost of our proposed algorithm is in O(n¹.5). We also propose a general rank- k update algorithm based upon the modified Sturm Theorem, and compare our results from those of the direct eigenvalue decomposition and of a perturbation method.

Citations

• MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education

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