Computing the Action of the Generating Function of Bernoulli Polynomials on a Matrix with An Application to Non-local Boundary Value Problems
<|reference_start|>Computing the Action of the Generating Function of Bernoulli Polynomials on a Matrix with An Application to Non-local Boundary Value Problems: This paper deals with efficient numerical methods for computing the action of the generating function of Bernoulli polynomials, say $q(\tau,w)$, on a typically large sparse matrix. This problem occurs when solving some non-local boundary value problems. Methods based on the Fourier expansion of $q(\tau,w)$ have already been addressed in the scientific literature. The contribution of this paper is twofold. First, we place these methods in the classical framework of Krylov-Lanczos (polynomial-rational) techniques for accelerating Fourier series. This allows us to apply the convergence results developed in this context to our function. Second, we design a new acceleration scheme. Some numerical results are presented to show the effectiveness of the proposed algorithms.<|reference_end|>
@article{aceto2024computing,
    title={Computing the Action of the Generating Function of Bernoulli Polynomials
  on a Matrix with An Application to Non-local Boundary Value Problems},
    author={Lidia Aceto, Luca Gemignani},
    journal={arXiv preprint arXiv:2406.01437},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.01437},
    primaryClass={math.NA cs.NA}
}