Efficient estimation of eigenvalue counts in an interval

2013/08/20 by Edoardo Di Napoli, Di Napoli, Edoardo, Eric Polizzi +3 · 4 citations
Computer Science · #FOS: Mathematics #Matrix Theory and Algorithms #Neural Networks and Applications #Numerical Analysis (math.NA) #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.1308.4275

openalex publication_date 2013/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an exact count is not necessary and methods based on stochastic estimates can be utilized to yield rough approximations. This paper examines a number of techniques tailored to this specific task. It reviews standard approaches and explores new ones based on polynomial and rational approximation filtering combined with a stochastic procedure.

Citations

• Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions

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