The short-term rational Lanczos method and applications

D Palitta, S Pozza, V Simoncini - SIAM Journal on Scientific Computing, 2022 - SIAM
Rational Krylov subspaces have become a reference tool in dimension reduction
procedures for several application problems. When data matrices are symmetric, a short …

Computation of generalized matrix functions with rational Krylov methods

A Casulli, I Simunec - Mathematics of Computation, 2023 - ams.org
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 …

Generation of orthogonal rational functions by procedures for structured matrices

N Van Buggenhout, M Van Barel, R Vandebril - Numerical Algorithms, 2022 - Springer
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 …

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 …

Gauss–Laurent-type quadrature rules for the approximation of functionals of a nonsymmetric matrix

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 …

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 …

Non-unitary CMV-decomposition

N Van Buggenhout, M Van Barel, R Vandebril - Special Matrices, 2020 - degruyter.com
Non-unitary CMV-decomposition Page 1 Open Access. © 2020 Niel Van Buggenhout et al.,
published by De Gruyter. This work is licensed under the Creative Commons Attribution …

[图书][B] Standard and Rational Gauss Quadrature Rules for the Approximation of Matrix Functionals

J Alahmadi - 2021 - search.proquest.com
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 …

Master thesis-Numerical Analysis

R Vandebril, N Van Buggenhout - wis.kuleuven.be
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 …