Zobrazeno 1 - 10
of 1 037
pro vyhledávání: '"Buggenhout, A."'
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities to advance quantum algorithms remain largely untapped. In this paper, we introduce effective implementations of rational transformations of a target oper
Externí odkaz:
http://arxiv.org/abs/2408.07742
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 the data better in attacking least squares problems, the ill-conditio
Externí odkaz:
http://arxiv.org/abs/2407.05945
In quantum mechanics, the Rosen-Zener model represents a two-level quantum system. Its generalization to multiple degenerate sets of states leads to larger non-autonomous linear system of ordinary differential equations (ODEs). We propose a new metho
Externí odkaz:
http://arxiv.org/abs/2311.04144
Autor:
Pozza, Stefano, Van Buggenhout, Niel
We introduce a new method with spectral accuracy to solve linear non-autonomous ordinary differential equations (ODEs) of the kind $ \frac{d}{dt}\tilde{u}(t) = \tilde{f}(t) \tilde{u}(t)$, $\tilde{u}(-1)=1$, with $\tilde{f}(t)$ an analytic function. T
Externí odkaz:
http://arxiv.org/abs/2303.11284
Autor:
Van Buggenhout, Niel
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 recurrence relation that can be represented by a Hessenberg matrix
Externí odkaz:
http://arxiv.org/abs/2302.10691
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 associated recurrence relations are computed. Moreover, also typ
Externí odkaz:
http://arxiv.org/abs/2302.00355
Autor:
Pozza, Stefano, Van Buggenhout, Niel
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in the scalar
Externí odkaz:
http://arxiv.org/abs/2210.07052
Autor:
Pozza, Stefano, Van Buggenhout, Niel
A new method for solving non-autonomous ordinary differential equations is proposed, the method achieves spectral accuracy. It is based on a new result which expresses the solution of such ODEs as an element in the so called $\star$-algebra. This alg
Externí odkaz:
http://arxiv.org/abs/2209.15533
Autor:
Pozza, Stefano, Van Buggenhout, Niel
Solving systems of non-autonomous ordinary differential equations (ODE) is a crucial and often challenging problem. Recently a new approach was introduced based on a generalization of the Volterra composition. In this work, we explain the main ideas
Externí odkaz:
http://arxiv.org/abs/2209.13322
The solution of linear non-autonomous ordinary differential equation systems (also known as the time-ordered exponential) is a computationally challenging problem arising in a variety of applications. In this work, we present and study a new framewor
Externí odkaz:
http://arxiv.org/abs/2206.03730