2007
DOI: 10.1016/j.cam.2006.02.041
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Spectral transformations for Hermitian Toeplitz matrices

Abstract: In this paper we deal with some perturbations of probability measures supported on the unit circle as well as, in a more general framework, with Hermitian linear functionals. We focus our attention in the Hessenberg matrix associated with the multiplication operator in terms of an orthogonal basis in the linear space of polynomials with complex coefficients. The LU and QR factorizations of such a matrix are introduced. Then, the connection between the above-mentioned perturbations and such factorizations is pr… Show more

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Cited by 33 publications
(45 citation statements)
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“…In [4] and [16] we have studied the connection between the associated Hessenberg matrices using the QR factorization. The iteration of the canonical Christoffel transformation has been analyzed in [8], [11], and [14].…”
Section: Introduction and Preliminary Resultsmentioning
confidence: 99%
See 2 more Smart Citations
“…In [4] and [16] we have studied the connection between the associated Hessenberg matrices using the QR factorization. The iteration of the canonical Christoffel transformation has been analyzed in [8], [11], and [14].…”
Section: Introduction and Preliminary Resultsmentioning
confidence: 99%
“…In [4] and [15] we have studied the connection between the corresponding sequences of monic orthogonal polynomials as well as the associated Hessenberg matrices using the LU and QR factorization. The iteration of the canonical Uvarov transformation has been studied in [7] and [14].…”
Section: Introduction and Preliminary Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…The analogues on the unit circle to the canonical spectral transformations on the real line have been introduced by Marcellán and co-workers; see [3,5,6,9,10] and are known in the literature by Christoffel, Geronimus and Uvarov. Our goal in this section is to study the zeros of polynomials generated by these three perturbations for Szegő.…”
Section: Zeros and Canonical Spectral Transformationsmentioning
confidence: 99%
“…A detailed study of the L-orthogonal polynomials {Q n } when ψ belongs to the class S 3 [0, β, b] was considered in Sri Ranga, Andrade and McCabe [13]. Some other aspects of these polynomials were also treated simultaneously in Common and McCabe [1].…”
Section: Introductionmentioning
confidence: 99%