Huertas, Edmundo J.Mañas Baena, Manuel Enrique2026-03-022026-03-022026-03E.J. Huertas, M. Mañas, Mixed-type multiple orthogonal Laurent polynomials on the unit circle, Journal of Computational and Applied Mathematics 475 (2026) 117037. https://doi.org/10.1016/j.cam.2025.117037.0377-042710.1016/j.cam.2025.117037https://hdl.handle.net/20.500.14352/1336382025 Acuerdos transformativos CRUE-CSIC © 2025 The Author(s). CM/JIN/2021-014 Programa Ayudas de Recualificación del Sistema Universitario Español para 2021–2023 (Convocatoria 2022)Mixed-type orthogonal Laurent polynomials on the unit circle of CMV type are constructed utilizing a matrix of moments and its Gauss–Borel factorization and employing a multiple extension of the CMV ordering. A systematic analysis of the associated multiple orthogonality and biorthogonality relations, and an examination of the degrees of the Laurent polynomials is given. Recurrence relations, expressed in terms of banded matrices, are found. These recurrence relations lay the groundwork for corresponding Christoffel–Darboux kernels and relations, as well as for elucidating the ABC theorem. The paper also develops the theory of diagonal Christoffel and Geronimus perturbations of the matrix of measures. Christoffel formulas are found for both perturbations.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal article1879-1778https://doi.org/10.1016/j.cam.2025.117037https://www.sciencedirect.com/science/article/pii/S0377042725005515open access530.1Mixed-type multiple orthogonal Laurent polynomialsUnit circleChristoffel–Darboux formulasABC theoremRecurrence relationsChristoffel perturbationsGeronimus perturbationsFísica-Modelos matemáticos2212 Física Teórica