Algorithms for modifying recurrence relations of orthogonal polynomial and rational functions when changing the discrete inner product
M Van Barel, N Van Buggenhout… - Applied Numerical …, 2024 - Elsevier
Often, polynomials or rational functions, orthogonal for a particular inner product are desired.
In practical numerical algorithms these polynomials are not constructed, but instead the …
In practical numerical algorithms these polynomials are not constructed, but instead the …
Rational QZ steps with perfect shifts
In this paper we analyze the stability of the problem of performing a rational QZ step with a
shift that is an eigenvalue of a given regular pencil H-λ K in unreduced Hessenberg …
shift that is an eigenvalue of a given regular pencil H-λ K in unreduced Hessenberg …
An Arnoldi-based approach to polynomial and rational least squares problems
A Faghih, M Van Barel, N Van Buggenhout… - arXiv preprint arXiv …, 2024 - arxiv.org
In this research, we solve polynomial, Sobolev polynomial, rational, and Sobolev rational
least squares problems. Although the increase in the approximation degree allows us to fit …
least squares problems. Although the increase in the approximation degree allows us to fit …
On generating Sobolev orthogonal polynomials
N Van Buggenhout - Numerische Mathematik, 2023 - Springer
Sobolev orthogonal polynomials are polynomials orthogonal with respect to a Sobolev inner
product, an inner product in which derivatives of the polynomials appear. They satisfy a long …
product, an inner product in which derivatives of the polynomials appear. They satisfy a long …
Structured matrix techniques for orthogonal rational functions and rational Krylov methods
N Van Buggenhout - 2021 - lirias.kuleuven.be
Polynomials are a powerful tool to approximate functions. If the function of interest does not
resemble a polynomial, rational function based methods might be more appropriate. The …
resemble a polynomial, rational function based methods might be more appropriate. The …