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Inverse Eigenvalue Problems for Complex Matrices
Computing, 1970Wir betrachten die Aufgabe, zu einer komplexen MatrixA eine DiagnonalmatrixV zu finden, so dasA+V (oderVA) vorgeschriebene komplexe Eigenwerte besitzt.
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On the Inverse Symmetric Quadratic Eigenvalue Problem
SIAM Journal on Matrix Analysis and Applications, 2014The detailed spectral structure of symmetric, algebraic, quadratic eigenvalue problems has been developed recently. In this paper we take advantage of these canonical forms to provide a detailed analysis of inverse problems of the following form: construct the coefficient matrices from the spectral data including the classical eigenvalue/eigenvector ...
Peter Lancaster, Ion Zaballa
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An inverse eigenvalue problem for Jacobi matrix
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ying Wei 0003, Hua Dai 0001
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An Inverse Eigenvalue Problem and an Extremal Eigenvalue Problem
1990This talk presents results for two inverse problems which arise in the study of vibrating systems. The first problem (Part I) extends the theory of second order inverse eigenvalue problems in one dimension and is joint work with Carol Coleman. The second problem (Part II) solves an identification problem for composite membranes in n-dimensions; this ...
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On the inversion of eigenvalue problems
Annals of Physics, 1963Abstract The aim of this paper is to draw attention to an apparently forgotten paper ( 1 ) on the inverse scattering problem in quantum mechanics and to add some generalizations and explanations. In the enormous literature ( 2, 3 ) which in the course of 15 years has grown up around this problem, nobody appears to have taken advantage of the simple ...
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On some structured inverse eigenvalue problems
Numerical Algorithms, 1997Two special structured inverse eigenvalue problems are investigated. The first one is the Jacobi inverse eigenvalue problem: given some constraints on two sets of reals, find a Jacobi matrix that admits as spectrum and principal subspectrum the two given sets. The polynomial algorithm is based on a special Euclid-Sturm algorithm.
Robert Erra, Bernard Philippe
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1996
Inverse eigenvalue problems are not only interesting in their own right but also have important practical applications. We recall the fundamental paper by Kac [132]. Other applications appear in parameter identification problems for parabolic or hyperbolic differential equations (see [149, 170, 234]) or in grating theory ([140]).
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Inverse eigenvalue problems are not only interesting in their own right but also have important practical applications. We recall the fundamental paper by Kac [132]. Other applications appear in parameter identification problems for parabolic or hyperbolic differential equations (see [149, 170, 234]) or in grating theory ([140]).
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An Inverse Eigenvalue Problem of Order Four
SIAM Journal on Mathematical Analysis, 1976In this paper coefficients $A(s) \in c^\infty [0,1]$, $B(s) \in c^\infty [0,1]$ are constructed so that given positive numbers $\lambda _1 < \lambda _2 < \cdots < \lambda _n $, are the first n eigenvalues and given positive numbers $\rho _1 , \cdots ,\rho _n $ are the first n normalization constants for the first n eigenfunctions for the fourth order ...
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The Additive Inverse Eigenvalue Problem for Lie Perturbations
SIAM Journal on Matrix Analysis and Applications, 1993The additive inverse eigenvalue problem over an algebraically closed field \(F\) of characteristic zero is considered: given a matrix \(A\in\text{gl}(n,F)\) and a matrix Lie subalgebra \({\mathcal L}\subset\text{gl}(n,F)\), under which conditions on \({\mathcal L}\) one can arbitrarily assign the eigenvalues of \(A+L\), when the perturbation \(L ...
Christopher I. Byrnes +1 more
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Backward errors for the inverse eigenvalue problem
Numerische Mathematik, 1999For a class of inverse symmetric eigenvalue problems, where real numbers \(c_1,\dots, c_n\) are sought, such that \(A_0+ \sum^n_{k= 1} c_kA_k\), where \(A_k\) are symmetric \(n\times n\) matrices, have certain prescribed eigenvalues, a computable backward error is given, which bounds the norms of symmetric perturbation matrices \(\Delta A_k\) mainly by
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