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of 596
pro vyhledávání: '"65j20"'
Autor:
Mathé, Peter, Hofmann, Bernd
The difficulty for solving ill-posed linear operator equations in Hilbert space is reflected by the strength of ill-posedness of the governing operator, and the inherent solution smoothness. In this study we focus on the ill-posedness of the operator
Externí odkaz:
http://arxiv.org/abs/2410.17729
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on energy co
Externí odkaz:
http://arxiv.org/abs/2410.11467
Autor:
Yang, Yanfei
The hybrid LSMR algorithm is proposed for large-scale general-form regularization. It is based on a Krylov subspace projection method where the matrix $A$ is first projected onto a subspace, typically a Krylov subspace, which is implemented via the G
Externí odkaz:
http://arxiv.org/abs/2409.09104
This paper shows that the Stokes problem is well-posed when both velocity and pressure vanish on the domain boundary. This result is achieved by extending Ne\v{c}as' inequality to square-integrable functions that vanish in a small band covering the b
Externí odkaz:
http://arxiv.org/abs/2407.15971
This paper proposes a data-driven approach for constructing firmly nonexpansive operators. We demonstrate its applicability in Plug-and-Play methods, where classical algorithms such as forward-backward splitting, Chambolle--Pock primal-dual iteration
Externí odkaz:
http://arxiv.org/abs/2407.14156
Autor:
Li, Yuanyuan, Lu, Shuai
We investigate a Tikhonov regularization scheme specifically tailored for shallow neural networks within the context of solving a classic inverse problem: approximating an unknown function and its derivatives within a unit cubic domain based on noisy
Externí odkaz:
http://arxiv.org/abs/2407.05078
Autor:
Monsuur, Harald, Stevenson, Rob
In this paper, conditional stability estimates are derived for unique continuation and Cauchy problems associated to the Poisson equation in ultra-weak variational form. Numerical approximations are obtained as minima of regularized least squares fun
Externí odkaz:
http://arxiv.org/abs/2407.04571
Autor:
Akwei, Bernard, Atkins, Bobita, Bailey, Rachel, Dalal, Ashka, Dinin, Natalie, Kerby-White, Jonathan, McGuinness, Tess, Patricks, Tonya, Rogers, Luke, Romanelli, Genevieve, Su, Yiheng, Teplyaev, Alexander
Eigenmaps are important in analysis, geometry, and machine learning, especially in nonlinear dimension reduction. Approximation of the eigenmaps of a Laplace operator depends crucially on the scaling parameter $\epsilon$. If $\epsilon$ is too small o
Externí odkaz:
http://arxiv.org/abs/2406.19510
Autor:
Hucker, Laura, Reiß, Markus
We consider estimators obtained by iterates of the conjugate gradient (CG) algorithm applied to the normal equation of prototypical statistical inverse problems. Stopping the CG algorithm early induces regularisation, and optimal convergence rates of
Externí odkaz:
http://arxiv.org/abs/2406.15001
In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results are: monotoni
Externí odkaz:
http://arxiv.org/abs/2406.07044