Influence functions related to eigenvalue problems which appear in multivariate analysis
作者： Yutaka Tanaka
DOI: 10.1080/03610928908830137
关键词: Mathematics 、 Symmetric matrix 、 Combinatorics 、 Eigendecomposition of a matrix 、 Eigenvalue perturbation 、 Eigenvalues and eigenvectors 、 Principal component analysis 、 Positive-definite matrix 、 Perturbation theory 、 Divide-and-conquer eigenvalue algorithm 、 Applied mathematics 、 Statistics and Probability
摘要: Tanaka(1988) derived two influence functions related to an ordinary eigenvalue problem (A–λs I)vs = 0 of a real symmetric matrix A and used them for sensitivity analysis in principal component analysis. One these was develop factor (see e.g. Tanaka Odaka, 1988a). The present paper derives some additional also several generalized (A–θs A)us 0, where B are positive definite matrices, respectively. These applicable not only the case eigenvalues interest all simple but there multiple among those interest.
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