منابع مشابه
Counting Fiedler pencils with repetitions
We introduce a new notation based on diagrams to deal with Fiedler pencils with repetitions (FPR), and use it to solve several counting problems. In particular, we give explicit recurrences to count the number of FPRs of a given degree d, the number of symmetric, palindromic and antipalindromic ones (where the latter two structures are intended in the sense of [5]). We relate these structures t...
متن کاملFiedler-comrade and Fiedler-Chebyshev pencils
Fiedler pencils are a family of strong linearizations for polynomials expressed in the monomial basis, that include the classical Frobenius companion pencils as special cases. We generalize the definition of a Fiedler pencil from monomials to a larger class of orthogonal polynomial bases. In particular, we derive Fiedler-comrade pencils for two bases that are extremely important in practical ap...
متن کاملA Unified Approach to Fiedler-like Pencils via Strong Block Minimal Bases Pencils
The standard way of solving the polynomial eigenvalue problem associated with a matrix polynomial is to embed the matrix polynomial into a matrix pencil, transforming the problem into an equivalent generalized eigenvalue problem. Such pencils are known as linearizations. Many of the families of linearizations for matrix polynomials available in the literature are extensions of the so-called fam...
متن کاملExplicit Block-structures for Block-symmetric Fiedler-like Pencils∗
In the last decade, there has been a continued effort to produce families of strong linearizations of a matrix polynomial P (λ), regular and singular, with good properties, such as, being companion forms, allowing the recovery of eigenvectors of a regular P (λ) in an easy way, allowing the computation of the minimal indices of a singular P (λ) in an easy way, etc. As a consequence of this resea...
متن کاملEla 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 (λ)x = 0, where P (λ) 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 (λ) due to the palindromicity are preserved. I...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2017
ISSN: 0024-3795
DOI: 10.1016/j.laa.2017.06.042