Geodesic
The CMV-matrix and the generalized Lanczos process
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 142-153
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The CMV-matrix is the five-diagonal matrix that represents the operator of multiplication by an independent variable in a special basis formed of Laurent polynomials orthogonal on the unit circle $C$. The article by Cantero, Moral, and Velázquez, which was published in 2003 and described this matrix, has attracted much attention because it implied that the conventional orthogonal polynomials on $C$ can be interpreted as the characteristic polynomials of the leading principal submatrices of a certain five-diagonal matrix. In this publication, we remind about the fact that finite-dimensional sections of the CMV-matrix emerged in papers on the unitary eigenvalue problem long before the article by Cantero et al. Moreover, band forms were also found for a number of other situations in the normal eigenvalue problem. 
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Kh. D. Ikramov. The CMV-matrix and the generalized Lanczos process. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 142-153. http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a10/

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