Work

Computing the action of the matrix generating function of Bernoulli polynomials on a vector with an application to non-local boundary value problems

Year: 2025

Type: article

Abstract: This paper deals with efficient numerical methods for computing the action of the matrix generating function of Bernoulli polynomials, say $$q(\tau ,A)$$ q ( τ , A ) , on a vector when A is a large and sparse matrix. This problem occurs when solving some non-local boundary value problems. Methods based on the Fourier expansion of $$q(\tau ,w)$$ 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.

Source: Advances in Computational Mathematics

DOI: 10.1007/s10444-025-10231-1

Authors: Lidia Aceto, Luca Gemignani

Institutions: Università degli Studi del Piemonte Orientale “Amedeo Avogadro”, University of Pisa

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190