A new look at the doubling algorithm for a structured palindromic quadratic eigenvalue problem. (English) Zbl 1363.65097
This paper proposes an improvement to the doubling algorithm for a structured palindromic quadratic eigenvalue problem [C.-H. Guo and W.-W. Lin, SIAM J. Matrix Anal. Appl. 31, No. 5, 2784–2801 (2010; Zbl 1215.65066)]. The key idea is replacing Guo and Lin’s key intermediate step by solving a new nonlinear matrix equation having the same form but of much smaller size. This leads to a faster algorithm. However, because of the cost in the other parts of the methods, the saving in the application of the doubling algorithm translates into a saving not so dramatic as just for solving the respective nonlinear matrix equations.
Reviewer: Liu Xinguo (Qingdao)
MSC:
| 65H17 | Numerical solution of nonlinear eigenvalue and eigenvector problems |
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 15A24 | Matrix equations and identities |
Keywords:
palindromic quadratic eigenvalue problem; nonlinear matrix equation; doubling algorithm; solvent approach; vibration analysis of high speed train; Matlab; LAPACKCitations:
Zbl 1215.65066References:
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