Publications related to Quantitative $ L ^{ 2 } $ Error Analysis for Interpolation Methods and Wavelet Expansions

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

Plug-and-play adaptive surrogate modeling of parametric nonlinear dynamics in frequency domain

Jürg Alexander Schiffmann, Phillip Huwiler, Davide Pradovera

We present an algorithm for constructing efficient surrogate frequency-domain models of (nonlinear) parametric dynamical systems in a non-intrusive way. To capture the dependence of the underlying system on frequency and parameters, our proposed approach c ...

2023

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Joao Pedro Gonçalves Ramos, Martin Peter Stoller

We obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Functional Tucker Approximation Using Chebyshev Interpolation

Daniel Kressner, Christoph Max Strössner

This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function approximations tha ...

SIAM PUBLICATIONS2021

MATHICSE Technical Report : Frequency-domain non-intrusive greedy Model Order Reduction based on minimal rational approximation

Fabio Nobile, Davide Pradovera

We present a technique for Model Order Reduction (MOR) of frequency-domain problems relying on rational interpolation of vector-valued functions. The selection of the sample points is carried out adaptively according to a greedy procedure. We describe seve ...

MATHICSE2020

Approximation of Non-decaying Signals from Shift-Invariant Subspaces

Michaël Unser, Quy Ha Nguyen

In our recent work, the sampling and reconstruction of non-decaying signals, modeled as members of weighted-L-p spaces, were shown to be stable with an appropriate choice of the generating kernel for the shift-invariant reconstruction space. In this paper, ...

2019

Regularity results for rough solutions of the incompressible Euler equations via interpolation methods

Maria Colombo, Luigi Forcella, Luigi De Rosa

Given any solutionuof the Euler equations which is assumed to have some regularity in space-in terms of Besov norms, natural in this context-we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure ...

IOP2019

Low-rank tensor methods for large Markov chains and forward feature selection methods

Francisco Santos Paredes Quartin de Macedo

In the first part of this thesis, we present and compare several approaches for the determination of the steady-state of large-scale Markov chains with an underlying low-rank tensor structure. Such structure is, in our context of interest, associated with ...

EPFL2018

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function

u

in multivariate polynomial spaces

P_\Lambda:=span\{y\mapsto y^\nu \,: \, \nu\in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma:=[-1,1]^d

, based on the s ...

2017

Attributing Aliasing Artifacts in Dirty Intensity Fields to their Parent Source

Matthieu Martin Jean-André Simeoni

Estimating intensity fields of stochastic phenomenons is of crucial interest in many scientific applications. Typical experimental setups involve an acquisition system, that subsequently filters and samples the probed intensity field. This equivalently def ...

2016

Quantitative $ L ^{ 2 } $ Error Analysis for Interpolation Methods and Wavelet Expansions

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Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Plug-and-play adaptive surrogate modeling of parametric nonlinear dynamics in frequency domain

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Functional Tucker Approximation Using Chebyshev Interpolation

MATHICSE Technical Report : Frequency-domain non-intrusive greedy Model Order Reduction based on minimal rational approximation

Approximation of Non-decaying Signals from Shift-Invariant Subspaces

Regularity results for rough solutions of the incompressible Euler equations via interpolation methods

Low-rank tensor methods for large Markov chains and forward feature selection methods

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Attributing Aliasing Artifacts in Dirty Intensity Fields to their Parent Source

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Plug-and-play adaptive surrogate modeling of parametric nonlinear dynamics in frequency domain

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Regularity results for rough solutions of the incompressible Euler equations via interpolation methods

Approximation of Non-decaying Signals from Shift-Invariant Subspaces

Functional Tucker Approximation Using Chebyshev Interpolation

Low-rank tensor methods for large Markov chains and forward feature selection methods

Attributing Aliasing Artifacts in Dirty Intensity Fields to their Parent Source

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

MATHICSE Technical Report : Frequency-domain non-intrusive greedy Model Order Reduction based on minimal rational approximation