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Recursive construction of biorthogonal polynomials for handling polynomial regression

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  • Rebollo-Neira, Laura
  • Laurie, Jason

Abstract

An adaptive procedure for constructing polynomials which are biorthogonal to the basis of monomials in the same finite-dimensional inner product space is proposed. By taking advantage of available orthogonal polynomials, the proposed methodology reduces the well-known instability problem arising from the matrix inversion involved in classical polynomial regression. The recurrent generation of the biorthogonal basis facilitates the upgrading of all its members to include an additional one. Moreover, it allows for a natural downgrading of the basis. This convenient feature leads to a straightforward approach for reducing the number of terms in the polynomial regression approximation. The merit of this approach is illustrated through a series of examples where the resulting biorthogonal basis is derived from Legendre, Laguerre, and Chebyshev orthogonal polynomials.

Suggested Citation

  • Rebollo-Neira, Laura & Laurie, Jason, 2025. "Recursive construction of biorthogonal polynomials for handling polynomial regression," Applied Mathematics and Computation, Elsevier, vol. 507(C).
    • Handle: RePEc:eee:apmaco:v:507:y:2025:i:c:s0096300325003042
    DOI: 10.1016/j.amc.2025.129578
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    References listed on IDEAS

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    1. Joakim Munkhammar & Lars Mattsson & Jesper Rydén, 2017. "Polynomial probability distribution estimation using the method of moments," PLOS ONE, Public Library of Science, vol. 12(4), pages 1-14, April.
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