Zobrazeno 1 - 10
of 164
pro vyhledávání: '"Beckermann, Bernhard"'
Publikováno v:
Numerical Algorithms, Springer Verlag, In press
We investigate the problem of approximating the matrix function $f(A)$ by $r(A)$, with $f$ a Markov function, $r$ a rational interpolant of $f$, and $A$ a symmetric Toeplitz matrix. In a first step, we obtain a new upper bound for the relative interp
Externí odkaz:
http://arxiv.org/abs/2106.05098
This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified
Externí odkaz:
http://arxiv.org/abs/2008.11501
Two central objects in constructive approximation, the Christoffel-Darboux kernel and the Christoffel function, are encoding ample information about the associated moment data and ultimately about the possible generating measures. We develop a multiv
Externí odkaz:
http://arxiv.org/abs/1812.06560
Autor:
Beckermann, Bernhard, Helart, Thomas
In this paper we show that the weighted Bernstein-Walsh inequality in logarithmic potential theory is sharp up to some new universal constant, provided that the external field is given by a logarithmic potential. Our main tool for such results is a n
Externí odkaz:
http://arxiv.org/abs/1707.07871
We consider the task of updating a matrix function $f(A)$ when the matrix $A\in{\mathbb C}^{n \times n}$ is subject to a low-rank modification. In other words, we aim at approximating $f(A+D)-f(A)$ for a matrix $D$ of rank $k \ll n$. The approach pro
Externí odkaz:
http://arxiv.org/abs/1707.03045
Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation - precisely the case where rational functions outperform polynomials by a landslide. We show that far more robust
Externí odkaz:
http://arxiv.org/abs/1705.10132
Matrices whose adjoint is a low rank perturbation of a rational function of the matrix naturally arise when trying to extend the well known Faber-Manteuffel theorem, which provides necessary and sufficient conditions for the existence of a short Arno
Externí odkaz:
http://arxiv.org/abs/1702.00671
Autor:
Beckermann, Bernhard, Townsend, Alex
Matrices with displacement structure such as Pick, Vandermonde, and Hankel matrices appear in a diverse range of applications. In this paper, we use an extremal problem involving rational functions to derive explicit bounds on the singular values of
Externí odkaz:
http://arxiv.org/abs/1609.09494
By exploiting a link between Bergman orthogonal polynomials and the Grunsky matrix, probably first observed by K{\"u}hnau in 1985, we improve some recent results on strong asymptotics of Bergman polynomials outside the domain G of orthogonality, and
Externí odkaz:
http://arxiv.org/abs/1606.00553
In this paper we consider the problem of working with rational functions in a numeric environment. A particular problem when modeling with such functions is the existence of Froissart doublets, where a zero is close to a pole. We discuss three differ
Externí odkaz:
http://arxiv.org/abs/1605.00506