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RMPIA: a new algorithm for computing the Lagrange matrix interpolation polynomials

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Abstract

Let σ0,σ1,⋯,σn be a set of n+ 1 distinct real numbers (i.e., σi≠σj, for i≠j) and F0,F1,⋯ ,Fn, be given real s × r matrices, we know that there exists a unique s × r matrix polynomial Pn(λ) of degree n such that Pn(σi) = Fi, for i = 0,1,⋯ ,n, Pn is the matrix interpolation polynomial for the set {(σi,Fi),i = 0,1,⋯ ,n}. The matrix polynomial Pn(λ) can be computed by using the Lagrange formula or the barycentric method. This paper presents a new method for computing matrix interpolation polynomials. We will reformulate the Lagrange matrix interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Recursive Matrix Polynomial Interpolation Algorithm (RMPIA) in full and simplified versions, and some properties of this algorithm will be studied. Cost and storage of this algorithm with the classical formulas will be studied and some examples will also be given.

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Acknowledgements

We would like to thank the referee for his helpful comments and valuable suggestions.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Informatique et Applications - Srité de l’Information (LabMiA-SI), Ecole Normale Supérieure, Mohammed V University in Rabat, Av. Mohammed Belhassan El Ouazzani, B.P. 5118, Takaddoum, Rabat, Morocco

    Abderrahim Messaoudi

  2. Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral Cote d’Opale, 50 rue F. Buisson BP 699, 62228, Calais Cedex, France

    Hassane Sadok

Authors
  1. Abderrahim Messaoudi
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  2. Hassane Sadok
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Correspondence to Abderrahim Messaoudi.

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Dedicated to the Professor Claude Brezinski for his 80th birthday

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Messaoudi, A., Sadok, H. RMPIA: a new algorithm for computing the Lagrange matrix interpolation polynomials. Numer Algor 92, 849–867 (2023). https://doi.org/10.1007/s11075-022-01357-0

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  • DOI: https://doi.org/10.1007/s11075-022-01357-0

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