Geodesic
Matrix orthogonal polynomials associated with perturbations of block Toeplitz matrices
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2017), pp. 66-79

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Let $\{c_j\}_{j=0}^{n}$ be a sequence of matrix moments associated with a matrix of measures supported on the unit circle, and let $\{P_j\}_{j=0}^{n}$ be its corresponding sequence of monic matrix orthogonal polynomials. In this contribution, we consider a perturbation on the moments and find an explicit relation for the perturbed orthogonal polynomials in terms of $\{P_j\}_{j=0}^{n}$. We also obtain an expression for the corresponding second kind polynomials.
Keywords: matrix orthogonal polynomials on the unit circle, moment problem, second kind polynomials, Toeplitz matrices. 
@article{IVM_2017_12_a6,
     author = {A. E. Choke Rivero and L. E. Garza Gaona},
     title = {Matrix orthogonal polynomials associated with perturbations of block {Toeplitz} matrices},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {66--79},
     publisher = {mathdoc},
     number = {12},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_12_a6/}
}
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%A L. E. Garza Gaona
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%D 2017
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A. E. Choke Rivero; L. E. Garza Gaona. Matrix orthogonal polynomials associated with perturbations of block Toeplitz matrices. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2017), pp. 66-79. http://geodesic.mathdoc.fr/item/IVM_2017_12_a6/