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 …

Quantum Rational Transformation Using Linear Combinations of Hamiltonian Simulations

Y Shen, N Van Buggenhout, D Camps… - arxiv preprint arxiv …, 2024 - arxiv.org
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities
to advance quantum algorithms remain largely untapped. In this paper, we introduce …

Deflated and restarted Krylov subspace methods for Sylvester tensor equations

Y Gu, G Wu, X Zhang - Calcolo, 2023 - Springer
Tensor Krylov subspace methods are popular technologies for solving Sylvester tensor
equations, among which the GMRES method based on tensor format (GMRES_BTF) and the …

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 …

[PDF][PDF] Biorthogonal rational Krylov subspace methods

A general framework for oblique projections of non-Hermitian matrices onto rational Krylov
subspaces is developed. To obtain this framework we revisit the classical rational Krylov …

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 …

Transformation and approximation of rational Krylov spaces with an application to 2.5-dimensional direct current resistivity modeling

S Stein - 2021 - tubaf.qucosa.de
Abstract (DE) Die vorliegende Arbeit befasst sich mit der Fragestellung, inwiefern sich
gegebene Verfahren zur Approximation von rationalen Krylow-Räumen zur Berechnung von …

Biorthogonal Extended Krylov Subspace Methods

N Van Buggenhout, M Van Barel… - arxiv preprint arxiv …, 2018 - arxiv.org
A general framework for oblique projections of nonhermitian matrices onto rational Krylov
subspaces is developed. To obtain this framework we revisit the classical rational Krylov …