Accurate computations with Wronskian matrices

Abstract

In this paper we provide algorithms for computing the bidiagonal decomposition of the Wronskian matrices of the monomial basis of polynomials and of the basis of exponential polynomials. It is also shown that these algorithms can be used to perform accurately some algebraic computations with these Wronskian matrices, such as the calculation of their inverses, their eigenvalues or their singular values and the solutions of some linear systems. Numerical experiments illustrate the results.

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Acknowledgements

This work was partially supported through the Spanish research grant PGC2018-096321-B-I00 (MCIU/AEI), by Gobierno de Aragón (E41\(\_\)17R ) and by Feder 2014–2020 “Construyendo Europa desde Aragón”.

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Correspondence to B. Rubio.

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Mainar, E., Peña, J.M. & Rubio, B. Accurate computations with Wronskian matrices. Calcolo 58, 1 (2021). https://doi.org/10.1007/s10092-020-00392-4

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Keywords

  • Accurate computations
  • Wronskian matrices
  • Bidiagonal decompositions