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Convergence of Eigenvector Continuation [PDF]
Phys. Rev. Lett. 126, 032501 (2021), 2020 Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to selected training values of the control parameters.
Avik Sarkar, Dean Lee
arxiv +6 more sources
On Differentiating Eigenvalues and Eigenvectors [PDF]
Econometric Theory, 1985 Let X0 be a square matrix (complex or otherwise) and u0 a (normalized) eigenvector associated with an eigenvalue λo of X0, so that the triple (X0, u0, λ0) satisfies the equations Xu = λu, . We investigate the conditions under which unique differentiable functions λ(X) and u(X) exist in a neighborhood of X0 satisfying λ(X0) = λO, u(X0) = u0, Xu = λu ...
Jan R. Magnus
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The rotation of eigenvectors by a perturbation—II
Journal of Mathematical Analysis and Applications, 1965 Although the behavior of the eigenvalues of a hermitian matrix under perturbation is fairly well understood, there has been almost nothing done on the behavior of the eigenvectors. It is well known that they vary analytically under analytic perturbations but for some purposes one would prefer sharp bounds on the distance between the eigenvectors of a ...
Chandler Davis
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Eigenvectors in bottleneck algebra
Linear Algebra and its Applications, 1992 AbstractLet (B, ⩽) be a nonempty, linearly ordered set without maximum and minimum, and (⊕, ⊗) = (max, min). A vector x is said to be an eigenvector of a square matrix A if A ⊗ x = x. The aim of the present paper is to characterize the eigenvectors by means of the associated graph of the matrix and to give bounds for the set of all eigenvectors.
Kataŕına Cechlárová
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Mathematical modeling of the eigenvibrations for the loaded shallow shell [PDF]
E3S Web of Conferences, 2023 The eigenvalue problems modeling of the eigenvibrations of the loaded shallow shell are studied. The asymptotic properties of the eigenvalues and eigenvectors are investigated in dependence on the load parameters.
Samsonov Anton, Solov’ev Sergey
doaj +1 more source
Journal of Spectral Imaging, 2022 Principal components analysis (PCA), maximum autocorrelation factors (MAF), minimum noise factors (MNF) and maximum difference factors (MDF) models are common factor-based models used for analysis of hyperspectral images.
Neal B. Gallagher
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Applied General Topology, 2022 In this paper, we present some results on fixed point index calculations for multivalued mappings and apply them to prove the existence of solutions to multivalued equations in ordered space, under flexible conditions for the positive eigenvalue.
Vo Viet Tri
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Spectral properties for a type of heptadiagonal symmetric matrices
AIMS Mathematics, 2023 In this paper we expressed the eigenvalues of a sort of heptadiagonal symmetric matrices as the zeros of explicit rational functions establishing upper and lower bounds for each of them. From the prescribed eigenvalues, we computed eigenvectors for these
João Lita da Silva
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A Globally Convergent MCA Algorithm by Generalized Eigen-Decomposition [PDF]
International Journal of Computational Intelligence Systems, 2011 Minor component analysis (MCA) are used in many applications such as curve and surface fitting, robust beam forming, and blind signal separation. Based on the generalized eigen-decomposition, we present a completely different approach that leads to ...
Jianbin Gao, Mao Ye, Jianping Li, Qi Xia
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Energies, 2021 Power systems may encounter disturbances during operation as a result of switching of various components, etc. Such perturbations include transformer tap-changing action, load variations, and line outages due to various types of faults of which an earth ...
Ewaoche John Okampo +2 more
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