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Quadratic decomposition of orthogonal polynomials: a matrix approach

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Abstract

We consider a scalar orthogonal polynomial set associated with a regular functional. Its quadratic decomposition allows us to consider 2×2 matrix orthogonal polynomials whose coefficients are the components of the mentioned decomposition. The connection between the recurrence relations is given.

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Authors and Affiliations

  1. Escuela Politécnica Superior, Universidad Carlos III, Leganés, 28913, Madrid, Spain

    Francisco Marcellán

  2. Departamento Matemática Aplicada, E.T.S. de Ingenieros Industriales, c/José Gutiérrez Abascal 2, 28006, Madrid, Spain

    Gabriela Sansigre

Authors
  1. Francisco Marcellán
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  2. Gabriela Sansigre
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Additional information

Partially supported by an “Acción Integrada Hispano-Portuguesa, no. 28 B/91”.

Realized in part during a stay in Paris, Lab. Analyse Numérique, Univ. Pierre et Marie Curie — CNRS, granted by MEC(Spain)/MRT(France) FR91.

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Marcellán, F., Sansigre, G. Quadratic decomposition of orthogonal polynomials: a matrix approach. Numer Algor 3, 285–298 (1992). https://doi.org/10.1007/BF02141937

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