The Experts below are selected from a list of 404142 Experts worldwide ranked by ideXlab platform
Li Jie-hong - One of the best experts on this subject based on the ideXlab platform.
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Inverse Problem of Generalized Eigenvalue for Nonnegtive Symmetric Tridiagonal Matrix
Journal of Tianjin University of Science and Technology, 2020Co-Authors: Li Jie-hongAbstract:we discuss a inverse problem of generalized Eigenvalue for nonnegtive symmetric tridiagonal matrix by giving part of Eigenvalues and corresponding eigenvectors.And we give the sufficient conditions for solubility of this problem.
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On the Generalized Eigenvalue of Nonegtive Period Symmetric Tridiagonal Matrix Inverse Problem
Journal of Tangshan College, 2020Co-Authors: Li Jie-hongAbstract:The paper discusses the generalized Eigenvalue of the nonegtive period symmetric tridiagonal matrix inverse problem by giving part of Eigenvalues and corresponding eigenvectors.
Colin P Williams - One of the best experts on this subject based on the ideXlab platform.
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Quantum Chemistry with a Quantum Computer
Explorations in Quantum Computing, 2011Co-Authors: Colin P WilliamsAbstract:In quantum chemistry, one is often interested in the static properties of a molecular quantum system, such its electronic structure, or its energy Eigenvalues and eigenstates. In this chapter we describe the Abrams-Lloyd and Kitaev Eigenvalue estimation algorithms. These provide efficient algorithms for determining the exact Eigenvalue associated with a given eigenstate, a feat that is exponentially more difficult to do classically to the same precision.
Sean P. Kenny - One of the best experts on this subject based on the ideXlab platform.
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Eigenvalue and Eigenvector Approximate Analysis for Repeated Eigenvalue Problems
AIAA Journal, 1992Co-Authors: Sean P. KennyAbstract:The method developed for approximate analysis involves a reparamaterization of the multivariable structural Eigenvalue problems in terms of a single positive-valued parameter. The resulting equations yield first order approximations of changes in both the Eigenvalues and eigenvectors associated with the repeated Eigenvalue problem.
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Eigenvalue and eigenvector sensitivity and approximate analysis for repeated Eigenvalue problems
32nd Structures Structural Dynamics and Materials Conference, 1991Co-Authors: Sean P. KennyAbstract:A set of computationally efficient equations for Eigenvalue and eigenvector sensitivity analysis are derived, and a method for Eigenvalue and eigenvector approximate analysis in the presence of repeated Eigenvalues is presented. The method developed for approximate analysis involves a reparamaterization of the multivariable structural Eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations of changes in both the Eigenvalues and eigenvectors associated with the repeated Eigenvalue problem. Examples are given to demonstrate the application of such equations for sensitivity and approximate analysis.
Lili Zhang - One of the best experts on this subject based on the ideXlab platform.
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recursive estimation for ordered eigenvectors of symmetric matrix with observation noise
Journal of Mathematical Analysis and Applications, 2011Co-Authors: Hanfu Chen, Haitao Fang, Lili ZhangAbstract:Abstract The principal component analysis is to recursively estimate the eigenvectors and the corresponding Eigenvalues of a symmetric matrix A based on its noisy observations A k = A + N k , where A is allowed to have arbitrary Eigenvalues with multiplicity possibly bigger than one. In the paper the recursive algorithms are proposed and their ordered convergence is established: It is shown that the first algorithm a.s. converges to a unit eigenvector corresponding to the largest Eigenvalue, the second algorithm a.s. converges to a unit eigenvector corresponding to either the second largest Eigenvalue in the case the largest Eigenvalue is of single multiplicity or the largest Eigenvalue if the multiplicity of the largest Eigenvalue is bigger than one, and so on. The convergence rate is also derived.
Daniel Kressner - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Eigenvalue Problems with Specified Eigenvalues
SIAM Journal on Matrix Analysis and Applications, 2014Co-Authors: Michael Karow, Daniel Kressner, Emre MengiAbstract:This work considers Eigenvalue problems that are nonlinear in the Eigenvalue parameter. Given such a nonlinear Eigenvalue problem $T$, we are concerned with finding the minimal backward error such that $T$ has a set of prescribed Eigenvalues with prescribed algebraic multiplicities. We consider backward errors that only allow constant perturbations, which do not depend on the Eigenvalue parameter. While the usual resolvent norm addresses this question for a single Eigenvalue of multiplicity one, the general setting involving several Eigenvalues is significantly more difficult. Under mild assumptions, we derive a singular value optimization characterization for the minimal perturbation that addresses the general case.
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Generalized Eigenvalue problems with specified Eigenvalues
Ima Journal of Numerical Analysis, 2013Co-Authors: Daniel Kressner, Emre Mengi, Ivica Nakić, Ninoslav TruharAbstract:We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specied Eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness for two applications. First, the characterization yields a singular value formula for determining the nearest pencil whose Eigenvalues lie in a specied region in the complex plane. For instance, this enables the numerical computation of the nearest stable descriptor system in control theory. Second, the characterization partially solves the problem posed in [Boutry et al. 2005] regarding the distance from a general rectangular pencil to the nearest pencil with a complete set of Eigenvalues. The involved singular value optimization problems are solved by means of BFGS and Lipschitz-based global optimization algorithms.
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Continuation of Eigenvalues and invariant pairs for parameterized nonlinear Eigenvalue problems
Numerische Mathematik, 2011Co-Authors: Wolf-jürgen Beyn, Cedric Effenberger, Daniel KressnerAbstract:Invariant pairs have been proposed as a numerically robust means to represent and compute several Eigenvalues along with the corresponding (generalized) eigenvectors for matrix Eigenvalue problems that are nonlinear in the Eigenvalue parameter. In this work, we consider nonlinear Eigenvalue problems that depend on an additional parameter and our interest is to track several Eigenvalues as this parameter varies. Based on the concept of invariant pairs, a theoretically sound and reliable numerical continuation procedure is developed. Particular attention is paid to the situation when the procedure approaches a singularity, that is, when Eigenvalues included in the invariant pair collide with other Eigenvalues. For the real generic case, it is proven that such a singularity only occurs when two Eigenvalues collide on the real axis. It is shown how this situation can be handled numerically by an appropriate expansion of the invariant pair. The viability of our continuation procedure is illustrated by a numerical example.
