Computing the Action of the Generating Function of Bernoulli Polynomials on a Matrix with An Application to Non-local Boundary Value Problems
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909764246568960 |
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| author | Aceto, Lidia Gemignani, Luca |
| author_facet | Aceto, Lidia Gemignani, Luca |
| contents | This paper deals with efficient numerical methods for computing the action of the generating function of Bernoulli polynomials, say $q(τ,w)$, on a typically large sparse matrix. This problem occurs when solving some non-local boundary value problems. Methods based on the Fourier expansion of $q(τ,w)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01437 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing the Action of the Generating Function of Bernoulli Polynomials on a Matrix with An Application to Non-local Boundary Value Problems Aceto, Lidia Gemignani, Luca Numerical Analysis 15A60, 65F60 This paper deals with efficient numerical methods for computing the action of the generating function of Bernoulli polynomials, say $q(τ,w)$, on a typically large sparse matrix. This problem occurs when solving some non-local boundary value problems. Methods based on the Fourier expansion of $q(τ,w)$ 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. |
| title | Computing the Action of the Generating Function of Bernoulli Polynomials on a Matrix with An Application to Non-local Boundary Value Problems |
| topic | Numerical Analysis 15A60, 65F60 |
| url | https://arxiv.org/abs/2406.01437 |