We present a class of algorithms based on rational Krylov methods to compute the action of a generalized matrix function on a vector. These algorithms incorporate existing methods …
The problem of computing recurrence coefficients of sequences of rational functions orthogonal with respect to a discrete inner product is formulated as an inverse eigenvalue …
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 …
J Alahmadi, H Alqahtani, MS Pranić, L Reichel - Numerical Algorithms, 2021 - Springer
This paper is concerned with the approximation of matrix functionals of the form w T f (A) v, where A∈ ℝ n× n A∈R^n*n is a large nonsymmetric matrix, w, v∈ ℝ nw,v∈R^n, and f is a …
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 …
In this thesis we develop efficient numerical methods for the approximation of matrix functionals of the form F (A):= w^ Tf (A) v, where A is a large symmetric or nonsymmetric …
This is an RII-type recurrence relation, which builds a pair of biorthogonal rational functions [?]. Meanwhile, in another field of mathematics, Krylov subspaces are studied and applied to …