PALINDROMIC LINEARIZATIONS OF A MATRIX POLYNOMIAL OF ODD DEGREE OBTAINED FROM FIEDLER PENCILS WITH REPETITION

Many applications give rise to structured, in particular T-palindromic, matrix polynomials. In order to solve a polynomial eigenvalue problem P(lambda)x = 0, where P(lambda) is a T-palindromic matrix polynomial, it is convenient to use palindromic linearizations to ensure that the symmetries in the eigenvalues, elementary divisors, and minimal indices of P(lambda) due to the palindromicity are preserved. In this paper, new T-palindromic strong linearizations valid for all palindromic matrix polynomials of odd degree are constructed. These linearizations are formulated in terms of Fiedler pencils with repetition, a new family of companion forms that was obtained recently by Antoniou and Vologiannidis.