A note on unimodular eigenvalues for palindromic eigenvalue problems

作者：Chiang Chun Yueh^*; Chu Eric King wah; Weng Chang Yi

来源：International Journal of Computer Mathematics, 2012, 89(17): 2385-2391.

DOI：10.1080/00207160.2012.709626

• palindromic eigenvalue problem
• structure-preserving doubling algorithm
• unimodular eigenvalue

We consider the occurrence of unimodular eigenvalues for palindromic eigenvalue problems associated with the matrix polynomial P-n(lambda) equivalent to Sigma(n)(i=0) A(i)lambda(i), where A(i)* = A(n-i) with M* equivalent to M-T, M-H or P (M) over barP (P-2 = I). From the properties of palindromic eigenvalues and their characteristic polynomials, we show that eigenvalues are not generically excluded from the unit circle, thus occurring quite often, except for the complex transpose case when P-n is complex and M* equivalent to M-T. This behaviour is observed in numerical simulations and has important implications on several applications such as the vibration of fast trains, surface acoustic wave filters, stability of time-delay systems and crack modelling.

• 出版日期2012