On the inverse symmetric quadratic eigenvalue problem
type: Item
instance of: scholarly article
zbMATH Open document ID: 1320.47007
DOI: 10.1137/130905216
author: P. Lancaster
author: Ion Zaballa
published in: SIAM Journal on Matrix Analysis and Applications
publication date: 2014-08-21T00:00:00Z
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 65F18
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 39A99
zbMATH DE Number: 6333368
zbMATH Keywords: symmetric matrix polynomials
zbMATH Keywords: inverse quadratic eigenvalue problem
zbMATH Keywords: self-adjoint Jordan triples
zbMATH Keywords: sign characteristic
MaRDI profile type: Publication
OpenAlex ID: W2072684432
title: On the inverse symmetric quadratic eigenvalue problem
review text: The inverse quadratic eigenvalue problem (IQEP) is to find a quadratic matrix polynomial \(L(\lambda)=L_2\lambda^2+L_1\lambda+L_0\) when eigenvalues are (partially) prescribed. The canonical Jordan form, developed in [the first author, ibid. 29, No. 1, 279--301 (2007; Zbl 1132.74017)] and the methods used there are completed in this paper to solve the real symmetric IQEP given the eigenvalues and a sign characteristic. Possibly extra positivity conditions on some coefficients of \(L(\lambda)\) can be prescribed. Essentially the semisimple case is considered, i.e., when algebraic and geometric multiplicities of the eigenvalues coincide. Conditions are given for \(L(\lambda)\) to be diagonalizable. This allows to formulate a procedure to generate not just one, but many different solutions.
reviewed by: Adhemar Bultheel
description: scientific article; zbMATH DE number 6333368