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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 906 (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 Contourlet Transform: An Efficient Directional Multiresolution Image Representation
 IEEE TRANSACTIONS ON IMAGE PROCESSING
"... The limitations of commonly used separable extensions of onedimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a “true” twodimensional transform that can capture the intrinsic geometrical structure t ..."
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Cited by 519 (20 self)
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flexible multiresolution, local, and directional image expansion using contour segments, and thus it is named the contourlet transform. The discrete contourlet transform has a fast iterated filter bank algorithm that requires an order N operations for Npixel images. Furthermore, we establish a precise
A multilinear singular value decomposition
 SIAM J. Matrix Anal. Appl
, 2000
"... Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are ..."
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Cited by 470 (22 self)
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Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc
Perturbative gauge theory as a string theory in twistor space
 COMMUN. MATH. PHYS
, 2003
"... Perturbative scattering amplitudes in YangMills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed ..."
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Cited by 384 (1 self)
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amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of N = 4 super YangMills theory and the Dinstanton expansion of a certain string theory, namely the topological B model whose target space is the Calabi
SENSITIVITY ANALYSIS FOR THE MULTIVARIATE EIGENVALUE PROBLEM
, 2013
"... This paper concerns with the sensitivity analysis for the multivariate eigenvalue problem (MEP). The concept of a simple multivariate eigenvalue of a matrix is generalized to the MEP and the firstorder perturbation expansions of a simple multivariate eigenvalue and the corresponding multivariate ..."
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This paper concerns with the sensitivity analysis for the multivariate eigenvalue problem (MEP). The concept of a simple multivariate eigenvalue of a matrix is generalized to the MEP and the firstorder perturbation expansions of a simple multivariate eigenvalue and the corresponding multivariate
Perturbation, Computation and Refinement of Invariant Pairs for Matrix Polynomials
, 2009
"... Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefi ..."
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Cited by 3 (2 self)
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under perturbations of the matrix polynomial is studied and a firstorder perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly
Perturbation, Extraction and Refinement of Invariant Pairs for Matrix Polynomials
, 2010
"... Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefi ..."
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Cited by 8 (2 self)
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of invariant pairs under perturbations of the matrix polynomial is studied and a firstorder perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement
Firstorder expansion of homogenized coefficients under Bernoulli perturbations
 J. Math. Pures Appl
, 2014
"... Abstract. Secondorder divergenceform operators with stationary random coefficients homogenize over large scales. We investigate the effect of certain perturbations of the medium on the homogenized coefficients. The perturbations that we consider are rare at the local level, but when occurring, hav ..."
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Cited by 3 (1 self)
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, have an effect of the same order of magnitude as the initial medium itself. The main result of the paper is a firstorder expansion of the homogenized coefficients, as a function of the perturbation parameter.
ISSN 17499097Perturbation, Computation and Refinement of Invariant Pairs for Matrix Polynomials
, 2009
"... Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefi ..."
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under perturbations of the matrix polynomial is studied and a firstorder perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly
The firstorder correction to the energy is
, 2004
"... These are working notes of the phenomenology of the 6p3/2 hyperfine structure in Cs, written to help with the analysis of experimental data. ..."
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These are working notes of the phenomenology of the 6p3/2 hyperfine structure in Cs, written to help with the analysis of experimental data.
Results 1  10
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