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On inverse eigenvalue problems of quadratic palindromic systems with partially prescribed eigenstructure. (English) Zbl 1427.65051

Summary: The palindromic inverse eigenvalue problem (PIEP) of constructing matrices \(A\) and \(Q\) of size \(n \times n\) for the quadratic palindromic polynomial \(P(\lambda) = \lambda^2 A^{\star} + \lambda Q + A\) so that \(P(\lambda)\) has \(p\) prescribed eigenpairs is considered. This paper provides two different methods to solve PIEP, and it is shown via construction that PIEP is always solvable for any \(p (1 \leq p \leq (3n+1)/2)\) prescribed eigenpairs. The eigenstructure of the resulting \(P(\lambda)\) is completely analyzed.

MSC:

65F18 Numerical solutions to inverse eigenvalue problems
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A24 Matrix equations and identities
15A29 Inverse problems in linear algebra

Software:

PEPACK
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References:

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