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Darboux transformation and perturbation of linear functionals
Abstract Let L be a quasi-definite linear functional defined on the linear space of polynomials with real coefficients. In the literature, three canonical transformations of this functional areExpand
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Palindromic linearizations of a matrix polynomial of odd degreee 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(�)x = 0, where P(�) is a T-palindromic matrixExpand
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Structured strong linearizations from Fiedler pencils with repetition I
Abstract In many applications, the polynomial eigenvalue problem, P ( λ ) x = 0 , arises with P ( λ ) being a structured matrix polynomial (for example, palindromic, symmetric, skew-symmetric). InExpand
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Large vector spaces of block-symmetric strong linearizations of matrix polynomials
Abstract Given a matrix polynomial P ( λ ) = ∑ i = 0 k λ i A i of degree k , where A i are n × n matrices with entries in a field F , the development of linearizations of P ( λ ) that preserveExpand
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A more accurate algorithm for computing the Christoffel transformation
A 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.Expand
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A simplified approach to Fiedler-like pencils via block minimal bases pencils
Abstract The standard way of solving the polynomial eigenvalue problem associated with a matrix polynomial is to embed the matrix coefficients of the polynomial into a matrix pencil, transforming theExpand
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Polynomial perturbations of bilinear functionals and Hessenberg matrices
This paper deals with symmetric and non-symmetric polynomial perturbations of symmetric quasi-definite bilinear functionals. We establish a relation between the Hessenberg matrices associated withExpand
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Eigenvectors and minimal bases for some families of Fiedler-like linearizations
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 familiesExpand
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Structured strong linearizations from Fiedler pencils with repetition II
Abstract In this paper we give strong linearizations of a matrix polynomial P ( λ ) preserving the skew-symmetry or T-alternating structure of P ( λ ) . The linearizations obtained are of the form SExpand
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CONTINUOUS SYMMETRIC SOBOLEV INNER PRODUCTS
In this paper we consider the sequence of monic polynomials (Qn) orthogonal with respect to a symmetric Sobolev inner product. If Q2n(x) = Pn(x) and Q2n+1(x) = xRn(x), then we deduce the integralExpand
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