Jarlebring, Elias; Kvaal, Simen; Michiels, Wim Computing all pairs \((\lambda , \mu )\) such that \(\lambda \) is a double eigenvalue of \(A+\mu B\). (English) Zbl 1245.65043 SIAM J. Matrix Anal. Appl. 32, No. 3, 902-927 (2011). The authors propose, analyze and test a method for the accurate numerical computation of the set of all scalar pairs \((\lambda ,\mu )\) such that \(\lambda\) is a multiple eigenvalue of \(A+\mu B\), where \(A\) and \(B\) are arbitrary given complex \(n\times n\) matrices. Emphasis is on the generic case in which \(\lambda\) is a double eigenvalue and the number of such pairs is finite but non-zero. First a global method is used to obtain approximations of all solutions by finding pairs \((\lambda ,\mu )\) for which both \(\lambda\) and \((1+\varepsilon )\lambda\) are eigenvalues, for some carefully chosen small \(\varepsilon\). Then a quadratically convergent iterative method (with different forms for the semisimple and non-semisimple cases) is used to refine the approximations. Reviewer: Alan L. Andrew (Bundoora) Cited in 9 Documents MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 15A22 Matrix pencils Keywords:double eigenvalue; two-parameter eigenvalue problem; regularization; iterative method × Cite Format Result Cite Review PDF Full Text: DOI Link