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BY 4.0 license Open Access Published by De Gruyter Open Access December 13, 2019

Numerical construction of structured matrices with given eigenvalues

  • Brian D. Sutton
From the journal Special Matrices

Abstract

We consider a structured inverse eigenvalue problem in which the eigenvalues of a real symmetric matrix are specified and selected entries may be constrained to take specific numerical values or to be nonzero. This includes the problem of specifying the graph of the matrix, which is determined by the locations of zero and nonzero entries. In this article, we develop a numerical method for constructing a solution to the structured inverse eigenvalue problem. The problem is recast as a constrained optimization problem over the orthogonal manifold, and a numerical optimization routine seeks its solution.

MSC 2010: 15A29; 65F18; 15A18; 15B99; 90C30

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Received: 2019-06-24
Accepted: 2019-11-30
Published Online: 2019-12-13

© 2019 Brian D. Sutton, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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