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(Received 00 Month 200x; in final form 00 Month 200x) In this paper we obtain formulas for the left and right eigenvectors and minimal bases of some families of Fiedler-like linearizations of square matrix polynomials. In particular, for the families of Fiedler pencils , generalized Fiedler pencils, and Fiedler pencils with repetition. These formulas allow(More)
A standard way to solve polynomial eigenvalue problems P (λ)x = 0 is to convert the matrix polynomial P (λ) into a matrix pencil that preserves its elementary divisors and, therefore, its eigenvalues. This process is known as linearization and is not unique, since there are infinitely many linearizations with widely varying properties associated with P (λ).(More)
The monic Jacobi matrix is a tridiagonal matrix which contains the parameters of the three-term recurrence relation satisfied by the sequence of monic polynomials orthogonal with respect to a measure. Darboux transformation without parameter changes a monic Jacobi matrix associated with a measure £ into the monic Jacobi matrix associated with ¤ ¦ ¥ § £.(More)
The development of strong linearizations preserving whatever structure a matrix polynomial might possess has been a very active area of research in the last years, since such lin-earizations are the starting point of numerical algorithms for computing eigenvalues of structured matrix polynomials with the properties imposed by the considered structure. In(More)
Given a symmetrized Sobolev inner product of order N , the corresponding sequence of monic orthogonal polynomials {Qn} satisfies Q 2n (x) = Pn(x 2), Q 2n+1 (x) = xRn(x 2) for certain sequences of monic polynomials {Pn} and {Rn}. In this paper we consider the particular case when all the measures that define the symmetrized Sobolev inner product are equal,(More)
Strong linearizations of a matrix polynomial P(λ) that preserve some structure of P(λ) are relevant in many applications. In this paper we characterize all the pencils in the family of the Fiedler pencils with repetition, introduced by Antoniou and Vologiannidis, associated with a square matrix polynomial P(λ) that are symmetric when P(λ) is. When some(More)
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