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Perturbation theory of eigenvalue problems

About: The article was published on 1969-01-01 and is currently open access. It has received 600 citations till now. The article focuses on the topics: Inverse iteration & Eigenvalue perturbation.
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Book
01 Apr 1988
TL;DR: In this article, the authors discuss the properties of Vectors and Matrices, the Vec-Operator, the Moore-Penrose Inverse Miscellaneous Matrix Results, and the Linear Regression Model.
Abstract: Preface MATRICES: Basic Properties of Vectors and Matrices Kronecker Products, the Vec-Operator and the Moore- Penrose Inverse Miscellaneous Matrix Results DIFFERENTIALS: THE THEORY: Mathematical Preliminaries Differentials and Differentiability The Second Differential Static Optimization DIFFERENTIALS: THE PRACTICE: Some Important Differentials First- Order Differentials and Jacobian Matrices Second-Order Differentials and Hessian Matrices INEQUALITIES: Inequalities THE LINEAR MODEL: Statistical Preliminaries The Linear Regression Model Further Topics in the Linear Model APPLICATIONS TO MAXIMUM LIKELIHOOD ESTIMATION: Maximum Likelihood Estimation Simultaneous Equations Topics in Psychometrics Subject Index Bibliography.

2,868 citations


Cites background from "Perturbation theory of eigenvalue p..."

  • ...Then, the eigenvalues are also continuous at t = 0 (Rellich 1953)....

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  • ...The relevant literature includes Rellich (1953) and Kato (1976, especially Theorems 1.10 and 5.1)....

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DOI
John Doyle1
01 Nov 1982
TL;DR: In this article, a general approach for analysing linear systems with structured uncertainty based on a new generalised spectral theory for matrices is introduced, which naturally extend techniques based on singular values and eliminate their most serious difficulties.
Abstract: The paper introduces a general approach for analysing linear systems with structured uncertainty based on a new generalised spectral theory for matrices. The results of the paper naturally extend techniques based on singular values and eliminate their most serious difficulties.

1,987 citations

Book
30 Sep 1997
TL;DR: Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly real compact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifold, infinite dimensional differential geometry Manifolds of Mappings Further applications References as mentioned in this paper.
Abstract: Introduction Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifolds Infinite dimensional differential geometry Manifolds of mappings Further applications References Index.

1,291 citations

Journal ArticleDOI
G.A. Watson1
TL;DR: In this article, a characterization of the subdifferential of matrix norms from two classes, orthogonally invariant norms and operator (or subordinate) norms, is given for some special cases.

429 citations

Journal ArticleDOI
TL;DR: It is shown that the performance of the proposed method tends to be close to that of the MMSE receiver at high SNR, whereas the constraint parameters converge to the multipath channel parameters.
Abstract: Constrained optimization of the receiver's output variance has previously been proposed as a relatively simple method for designing blind multiuser detectors for DS-CDMA systems. A single constraint is sufficient for the AWGN case, whereas multiple constraints should be used in a multipath environment. It is shown in this paper that the choice of the constraint parameters in the multipath case can have a significant effect on the system performance. A max/min approach for optimizing the constraint is proposed, resulting in blind solutions with improved performance. It is shown that the performance of the proposed method tends to be close to that of the MMSE receiver at high SNR, whereas the constraint parameters converge to the multipath channel parameters. The proposed method does not require knowledge of the interfering users' codes and timing. Simulation results support those performance claims.

329 citations


Cites background from "Perturbation theory of eigenvalue p..."

  • ...According to perturbation theory [13], if a matrix can be expressed as...

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