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pro vyhledávání: '"Vasseur Xavier"'
A general error analysis for randomized low-rank approximation with application to data assimilation
Randomized algorithms have proven to perform well on a large class of numerical linear algebra problems. Their theoretical analysis is critical to provide guarantees on their behaviour, and in this sense, the stochastic analysis of the randomized low
Externí odkaz:
http://arxiv.org/abs/2405.04811
We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we derive error bo
Externí odkaz:
http://arxiv.org/abs/2206.08793
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of inf
Externí odkaz:
http://arxiv.org/abs/2007.08326
Given a full column rank matrix $A \in \mathbb{R}^{m\times n}$ ($m\geq n$), we consider a special class of linear systems of the form $A^\top Ax=A^\top b+c$ with $x, c \in \mathbb{R}^{n}$ and $b \in \mathbb{R}^{m}$. The occurrence of $c$ in the right
Externí odkaz:
http://arxiv.org/abs/1911.00026
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently proposed in the l
Externí odkaz:
http://arxiv.org/abs/1904.04692
This paper is concerned with the approximation of the solution of partial differential equations by means of artificial neural networks. Here a feedforward neural network is used to approximate the solution of the partial differential equation. The l
Externí odkaz:
http://arxiv.org/abs/1904.04685
In this paper we present deflation and augmentation techniques that have been designed to accelerate the convergence of Krylov subspace methods for the solution of linear systems of equations. We review numerical approaches both for linear systems wi
Externí odkaz:
http://arxiv.org/abs/1303.5692
Publikováno v:
In Journal of Computational Physics 15 May 2017 337:379-402
Autor:
Toselli, Andrea, Vasseur, Xavier
Publikováno v:
COMPEL -The international journal for computation and mathematics in electrical and electronic engineering, 2005, Vol. 24, Issue 2, pp. 396-407.
Externí odkaz:
http://www.emeraldinsight.com/doi/10.1108/03321640510586033
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