The constrained inverse eigenvalue problem and its approximation for normal matrices

Peng, Xiangyang; Xiong, Huijun; Liu, Wei

doi:10.1016/j.laa.2011.05.028

Cited by 6 publications

(4 citation statements)

References 7 publications

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“…Centrosymmetric matrices are applied in information theory, linear system theory, and numerical analysis theory [9]. e unconstrained centrosymmetric matrices' problems have been discussed [9][10][11][12][13][14], a class of unconstrained matrices' inverse eigenproblems has been obtained [15][16][17][18], and the constrained inverse eigenproblems have been discussed [19][20][21][22], but only when the eigenvalues are real or imaginary numbers. For general real matrices, the eigenvalues are not necessarily real or imaginary numbers, so when the eigenvalue is complex, it is difficult to find the constraint solution.…”

Section: Introductionmentioning

confidence: 99%

The Centrosymmetric Matrices of Constrained Inverse Eigenproblem and Optimal Approximation Problem

Shen

Liu

Wang

et al. 2020

Mathematical Problems in Engineering

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In this paper, a kind of constrained inverse eigenproblem and optimal approximation problem for centrosymmetric matrices are considered. Necessary and sufficient conditions of the solvability for the constrained inverse eigenproblem of centrosymmetric matrices in real number field are derived. A general representation of the solution is presented for a solvable case. The explicit expression of the optimal approximation problem is provided. Finally, a numerical example is given to illustrate the effectiveness of the method.

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Section: Introductionmentioning

confidence: 99%

The Centrosymmetric Matrices of Constrained Inverse Eigenproblem and Optimal Approximation Problem

Shen

Liu

Wang

et al. 2020

Mathematical Problems in Engineering

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“…The results on the unconstrained inverse eigenvalue problem with several sets of matrices have been discussed [10−15] . Pan [7−8] and Peng [16] discussed the constrained inverse eigenvalue problem and associated approximation problems of antisymmetric matrices, skew symmetric and centrosymmetric matrices and normal matrices, respectively.…”

Section: Introductionmentioning

confidence: 99%

A class of constrained inverse eigenvalue problem and associated approximation problem for symmetrizable matrices

Peng

Wei

Shen

2019

Filomat

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The real symmetric matrix is widely applied in various fields, transforming non-symmetric matrix to symmetric matrix becomes very important for solving the problems associated with the original matrix. In this paper, we consider the constrained inverse eigenvalue problem for symmetrizable matrices, and obtain the solvability conditions and the general expression of the solutions. Moreover, we consider the corresponding optimal approximation problem, obtain the explicit expressions of the optimal approximation solution and the minimum norm solution, and give the algorithm and corresponding computational example.

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“…Peng et al. studied the constrained inverse eigenvalue problem for normal matrices . In , the numerical solutions of the inverse eigenvalue problem with Toeplitz matrices were studied.…”

Section: Introductionmentioning

confidence: 99%

“…Based on matrix equations, Aishima introduced a quadratically convergent algorithm for inverse symmetric eigenvalue problems [32]. Peng et al studied the constrained inverse eigenvalue problem for normal matrices [33]. In [34,35], the numerical solutions of the inverse eigenvalue problem with Toeplitz matrices were studied.…”

Section: Introductionmentioning

confidence: 99%

BCR Algorithm for Solving Quadratic Inverse Eigenvalue Problems for Partially Bisymmetric Matrices

Hajarian

2018

Asian Journal of Control

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The inverse eigenvalue problem appears repeatedly in a variety of applications. The aim of this paper is to study a quadratic inverse eigenvalue problem of the form AXΛ2 + BXΛ + CX = 0 where A, B and C should be partially bisymmetric under a prescribed submatrix constraint. We derive an efficient matrix method based on the Hestenes‐Stiefel (HS) version of biconjugate residual (BCR) algorithm for solving this constrained quadratic inverse eigenvalue problem. The theoretical results demonstrate that the matrix method solves the constrained quadratic inverse eigenvalue problem within a finite number of iterations in the absence of round‐off errors. Finally we validate the accuracy and efficiency of the matrix method through the numerical results.

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The constrained inverse eigenvalue problem and its approximation for normal matrices

Cited by 6 publications

References 7 publications

The Centrosymmetric Matrices of Constrained Inverse Eigenproblem and Optimal Approximation Problem

The Centrosymmetric Matrices of Constrained Inverse Eigenproblem and Optimal Approximation Problem

A class of constrained inverse eigenvalue problem and associated approximation problem for symmetrizable matrices

BCR Algorithm for Solving Quadratic Inverse Eigenvalue Problems for Partially Bisymmetric Matrices

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