Low rank approximation in the computation of first kind integral equations with TauToolbox

• Type: Article in International Scientific Journal
• Date: 2024

Authors

vasconcelos, pb (Author) FEP; Grammont, L (Author) Other; Lima, J (Author) Other

Journal

Title: Applied Numerical Mathematics

Vol. 205

Pages: 1-15

ISSN: 0168-9274

Publisher: Elsevier

Indexing

Scopus - 0 Citations

Other information

Authenticus ID: P-010-QY0

DOI: 10.1016/j.apnum.2024.06.022

Abstract (EN): Tau Toolbox is a mathematical library for the solution of integro-differential problems, based on the spectral Lanczos' Tau method. Over the past few years, a class within the library, called polynomial, has been developed for approximating functions by classical orthogonal polynomials and it is intended to be an easy-to-use yet efficient object-oriented framework. In this work we discuss how this class has been designed to solve linear ill-posed problems and we provide a description of the available methods, Tikhonov regularization and truncated singular value expansion. For the solution of the Fredholm integral equation of the first kind, which is built from a low-rank approximation of the kernel followed by a numerical truncated singular value expansion, an error estimate is given. Numerical experiments illustrate that this approach is capable of efficiently compute good approximations of linear discrete ill-posed problems, even facing perturbed available data function, with no programming effort. Several test problems are used to evaluate the performance and reliability of the solvers. The final product of this paper is the numerical solution of a first-kind integral equation, which is constructed using only two inputs from the user: the kernel and the right-hand side. © 2024 The Author(s)

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14