Fully Computable Error Bounds for Eigenvalue Problem

2016/01/07 by Hehu Xie, Xie, Hehu, Meiling Yue +3
Computer Science · Engineering · #65B99 #65L15 #65N25 #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.1601.01561

openalex publication_date 2016/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an asymptotically lower bound of the general eigenvalues. Furthermore, we also give a guaranteed upper bound of the error estimates for the first eigenfunction approximation and a guaranteed lower bound of the first eigenvalue based on computable error estimator. Some numerical examples are presented to validate the theoretical results deduced in this paper.

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