Perturbation of spectral subspaces and solution of linear operator equations
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In this article, it was shown that the spectrum of B can be obtained from that of A (multiplicities counted) by moving each eigenvalue by at most ϵ.About:
This article is published in Linear Algebra and its Applications.The article was published on 1983-07-01 and is currently open access. It has received 148 citations till now.read more
Citations
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Methodology and convergence rates for functional linear regression
TL;DR: In this paper, an alternative approach based on quadratic regularisation is suggested and shown to have advantages from some points of view, and it is shown that optimal convergence rates are achieved by the PCA technique in certain circumstances.
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Prediction in functional linear regression
T. Tony Cai,Peter Hall +1 more
TL;DR: In this paper, the authors proposed a method to solve the same problem with the help of NSF Grant DMS-03-06576 and a grant from the Australian Research Council.
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Properties of principal component methods for functional and longitudinal data analysis
TL;DR: In this article, the authors show that if there is a sample of n functions, or subjects, then estimation of eigenvalues is a semiparametric problem, with root-n consistent estimators, even if only a few observations are made of each function, and if each observation is encumbered by noise.
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On properties of functional principal components analysis
TL;DR: In this paper, the properties of functional principal component analysis can be elucidated through stochastic expansions and related results, which can be used to explore properties of existing methods, and also to suggest new techniques.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
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The Rotation of Eigenvectors by a Perturbation. III
Chandler Davis,William Kahan +1 more
TL;DR: In this article, the difference between the two subspaces is characterized in terms of certain angles through which one subspace must be rotated in order most directly to reach the other, and Sharp bounds upon trigonometric functions of these angles are obtained from the gap and from bounds upon either the perturbation or a computable residual.
Book
Introduction to Graph Theory
TL;DR: In this paper, Paths and cycles, trees, planarity, and coloring graphs are defined and examples of path-and-cycle exercises are given, together with solutions to selected exercises.