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Communication Dans Un Congrès Année : 2019

Taylor Series Revisited

Résumé

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 et versions

hal-02950743 , version 1 (28-09-2020)

Identifiants

  • HAL Id : hal-02950743 , version 1
  • OATAO : 26358

Citer

Xavier Thirioux, Alexis Maffart. Taylor Series Revisited. International Colloquium on Theoretical Aspects of Computing (ICTAC 2019), Oct 2019, Hammamet, Tunisia. pp.335-352. ⟨hal-02950743⟩
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