Search Results - "MATHÉ, PETER"

Inverse learning in Hilbert scales by Rastogi, Abhishake, Mathé, Peter

“…We study linear ill-posed inverse problems with noisy data in the framework of statistical learning. The corresponding linear operator equation is assumed to…”
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Tractability of linear ill-posed problems in Hilbert space by Mathé, Peter, Hofmann, Bernd

“…We introduce a notion of tractability for ill-posed operator equations in Hilbert space. For such operator equations the asymptotics of the best possible rate…”
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Designing truncated priors for direct and inverse Bayesian problems by Agapiou, Sergios, Mathé, Peter

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Two-layer networks with the ReLUk activation function: Barron spaces and derivative approximation by Li, Yuanyuan, Lu, Shuai, Mathé, Peter, Pereverzev, Sergei V.

“…We investigate the use of two-layer networks with the rectified power unit, which is called the ReLU k activation function, for function and derivative…”
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Optimal rates for Lavrentiev regularization with adjoint source conditions by Plato, Robert, Mathé, Peter, Hofmann, Bernd

“…There are various ways to regularize ill-posed operator equations in Hilbert space. If the underlying operator is accretive, then Lavrentiev regularization…”
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Complexity of linear ill-posed problems in Hilbert space by Mathé, Peter, Pereverzev, Sergei V.

“…Information complexity of ill-posed problems may be seen as controversial. On the one hand side there were pessimistic results stating that the complexity is…”
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Convergence analysis of Tikhonov regularization for non-linear statistical inverse problems by Rastogi, Abhishake, Blanchard, Gilles, Mathé, Peter

“…We study a non-linear statistical inverse problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points…”
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Discrepancy based model selection in statistical inverse problems by Lu, Shuai, Mathé, Peter

“…The reconstruction of solutions in statistical inverse problems in Hilbert spaces requires regularization, which is often based on a parametrized family of…”
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Adaptive discretization for signal detection in statistical inverse problems by Mathe, Peter

“…We discuss statistical tests in inverse problems when the original equation is replaced by a discretized one, i.e. a linear system of equations. Previous…”
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Analysis of Profile Functions for General Linear Regularization Methods by Hofmann, Bernd, Mathé, Peter

“…The stable approximate solution of ill-posed linear operator equations in Hilbert spaces requires regularization. Tight bounds for the noise-free part of the…”
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Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces by Anzengruber, Stephan W., Hofmann, Bernd, Mathé, Peter

“…The stable solution of ill-posed non-linear operator equations in Banach space requires regularization. One important approach is based on Tikhonov…”
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Heuristic parameter selection based on functional minimization: Optimality and model function approach by LU, SHUAI, MATHÉ, PETER

“…We analyze some parameter choice strategies in regularization of inverse problems, in particular, the (modified) L-curve method and a variant of the Hanke-Raus…”
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Regularization of some linear ill-posed problems with discretized random noisy data by Mathé, Peter, Pereverzev, Sergei V.

“…For linear statistical ill-posed problems in Hilbert spaces we introduce an adaptive procedure to recover the unknown solution from indirect discrete and noisy…”
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Simple Monte Carlo and the Metropolis algorithm by Mathé, Peter, Novak, Erich

“…We study the integration of functions with respect to an unknown density. Information is available as oracle calls to the integrand and to the non-normalized…”
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Discretized Lavrent'ev regularization for the autoconvolution equation by Bürger, Steven, Mathé, Peter

“…Lavrent'ev regularization for the autoconvolution equation was considered by Janno J. in Lavrent'ev regularization of ill-posed problems containing nonlinear…”
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Influence of the carrier reservoir dimensionality on electron-electron scattering in quantum dot materials by Wilms, Alexander, Mathé, Peter, Schulze, Franz, Koprucki, Thomas, Knorr, Andreas, Bandelow, Uwe

“…We calculated Coulomb scattering rates from quantum dots (QDs) coupled to a two-dimensional (2D) carrier reservoir and QDs coupled to a three-dimensional (3D)…”
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Direct and inverse results in variable Hilbert scales by Mathé, Peter, Hofmann, Bernd

“…Variable Hilbert scales are an important tool for the recent analysis of inverse problems in Hilbert spaces, as these constitute a way to describe smoothness…”
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The use of higher order finite difference schemes is not dangerous by Mathé, Peter, Pereverzev, Sergei V.

“…We discuss the issue of choosing a finite difference scheme for numerical differentiation in case the smoothness of the underlying function is unknown. If low…”
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Saturation of Regularization Methods for Linear Ill-Posed Problems in Hilbert Spaces by Mathe, Peter

“…We prove the saturation of methods for solving linear ill-posed problems in Hilbert spaces for a wide class of regularization methods. It turns out that, under…”
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A different perspective on the Propagation-Separation Approach by Becker, Saskia M. A., Mathé, Peter

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