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Reports (Technical Report) Year : 2020

Taylor Series Revisited

Abstract

We propose a renovated approach around the use of Taylor expansions to provide polynomial approximations. We introduce a coinductive type scheme and finely-tuned operations that altogether constitute an algebra, where our multivariate Taylor expansions are first-class objects. As for applications, beyond providing classical expansions of integro-differential and algebraic expressions mixed with elementary functions, we demonstrate that solving ODE and PDE in a direct way, without external solvers, is also possible. We also discuss the possibility of computing certified errors within our scheme.
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Dates and versions

hal-04357221 , version 1 (21-12-2023)

Identifiers

  • HAL Id : hal-04357221 , version 1
  • OATAO : 26670

Cite

Xavier Thirioux, Alexis Maffart. Taylor Series Revisited. ISAE/DISC/RT2020/1, Institut Supérieur de l'Aéronautique et de l'Espace. 2020. ⟨hal-04357221⟩
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