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Rank Test Based On Matrix Perturbation Theory
, 2001
"... In this paper, we propose methods of the determination of the rank of matrix. We consider a rank test for an unobserved matrix for which an estimate exists having normal asymptotic distribution of order N1/2where N is the sample size. The test statistic is based on the smallest estimated singular va ..."
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Cited by 3 (0 self)
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values. Using Matrix Perturbation Theory, the smallest singular values of random matrix converge asymptotically to zero in the order O(N31) and the corresponding left and right singular vectors converge asymptotically in the order O(N31/2). Moreover, the asymptotic distribution of the test statistic
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 907 (36 self)
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. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating
The use of matrix perturbation theory for addressing sensitivity and uncertainty issues in LCA
 In: Proceedings of The Fifth International Conference on EcoBalance  Practical
"... LCA, even when modeled in the traditional way with linear equations, may show strong nonlinear sensitivities. Welldeveloped tools from matrix perturbation theory may be employed to investigate LCA systems for the presence and location of such extreme sensitivities. This knowledge is useful for sta ..."
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Cited by 1 (1 self)
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LCA, even when modeled in the traditional way with linear equations, may show strong nonlinear sensitivities. Welldeveloped tools from matrix perturbation theory may be employed to investigate LCA systems for the presence and location of such extreme sensitivities. This knowledge is useful
Raamsdonk, “Matrix perturbation theory for Mtheory on a ppwave,” hepth/0205185
"... In this paper, we study the matrix model proposed by Berenstein, Maldacena, and Nastase to describe Mtheory on the maximally supersymmetric ppwave. We show that the model may be derived directly as a discretized theory of supermembranes in the ppwave background, or alternatively, from the dynamic ..."
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Cited by 133 (14 self)
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In this paper, we study the matrix model proposed by Berenstein, Maldacena, and Nastase to describe Mtheory on the maximally supersymmetric ppwave. We show that the model may be derived directly as a discretized theory of supermembranes in the ppwave background, or alternatively, from
On Spectral Clustering: Analysis and an algorithm
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS
, 2001
"... Despite many empirical successes of spectral clustering methods  algorithms that cluster points using eigenvectors of matrices derived from the distances between the points  there are several unresolved issues. First, there is a wide variety of algorithms that use the eigenvectors in slightly ..."
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Cited by 1713 (13 self)
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in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze
Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 892 (13 self)
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is the investigation of the relation between properties of a graph and the spectrum of its adjacency matrix. A central topic and important source of tools is the theory of association schemes. An association scheme is, roughly speaking, a collection of graphs on a common vertex set which fit together in a highly
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 607 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
The geometry of algorithms with orthogonality constraints
 SIAM J. MATRIX ANAL. APPL
, 1998
"... In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal proces ..."
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Cited by 640 (1 self)
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of previously unrelated algorithms. It is our hope that developers of new algorithms and perturbation theories will benefit from the theory, methods, and examples in this paper.
RealTime Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations
"... A key challenge for neural modeling is to explain how a continuous stream of multimodal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrateandfire neurons in realtime. We propose a new computational model for realtime computing on timevar ..."
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Cited by 469 (38 self)
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varying input that provides an alternative to paradigms based on Turing machines or attractor neural networks. It does not require a taskdependent construction of neural circuits. Instead it is based on principles of high dimensional dynamical systems in combination with statistical learning theory, and can
Multivariable Feedback Control: Analysis
 span (B∗) und Basis B∗ = { ω1
, 2005
"... multiinput, multioutput feedback control design for linear systems using the paradigms, theory, and tools of robust control that have arisen during the past two decades. The book is aimed at graduate students and practicing engineers who have a basic knowledge of classical control design and st ..."
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Cited by 564 (24 self)
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and statespace control theory for linear systems. A basic knowledge of matrix theory and linear algebra is required to appreciate and digest the material offered. This edition is a revised and expanded version of the first edition, which was published in 1996. The size of the
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