RELATIVE PERTURBATION THEORY FOR DIAGONALLY DOMINANT MATRICES
作者： Megan Dailey , Froilán M. Dopico , Qiang Ye
DOI: 10.1137/130943613
关键词: Mathematics 、 Linear algebra 、 Mathematical analysis 、 Linear system 、 Condition number 、 Eigenvalues and eigenvectors 、 Factorization 、 Singular value 、 Diagonally dominant matrix 、 Positive-definite matrix
摘要: In this paper, strong relative perturbation bounds are developed for a number of linear algebra problems involving diagonally dominant matrices. The key point is to parameterize matrices using their off-diagonal entries and parts consider small componentwise perturbations these parameters. This allows us obtain new the inverse, solution systems, symmetric indefinite eigenvalue problem, singular value nonsymmetric problem. These much stronger than traditional results, since they independent either standard condition or magnitude eigenvalues/singular values. Together with previously derived LDU factorization positive definite paper presents complete detailed account structured theory
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