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Domain-Informed Spline Interpolation

Publications associées (28)

Model order reduction based on functional rational approximants for parametric PDEs with meromorphic structure

Many engineering fields rely on frequency-domain dynamical systems for the mathematical modeling of physical (electrical/mechanical/etc.) structures. With the growing need for more accurate and reliable results, the computational burden incurred by frequen ...

EPFL2021

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

Computation of "Best" Interpolants in the Lp Sense

Michaël Unser, Pakshal Narendra Bohra

We study a variant of the interpolation problem where the continuously defined solution is regularized by minimizing the L p -norm of its second-order derivative. For this continuous-domain problem, we propose an exact discretization scheme that restricts ...

2020

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Michaël Unser, Pakshal Narendra Bohra

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

2020

Examining the Effects of Privacy-Aware Blended Learning Scenarios in Executive Training for Policymakers and Government Officials

Denis Gillet, Isabelle Barbara Marie-Hélène Cardia, Maria Gaci, Juan Carlos Farah

Enabling blended learning scenarios that foster participation and interaction is an important consideration in the design of executive training programs. To investigate this design process, our study focuses on two aspects that are present in such scenario ...

Springer2020

Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing

Daniel Kressner, Francesco Statti, Kathrin Beatrice Glau

Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately and in real-time. ...

2020

Characterization of the traces on the boundary of functions in magnetic Sobolev spaces

Hoài-Minh Nguyên

We characterize the trace of magnetic Sobolev spaces defined in a half-space or in a smooth bounded domain in which the magnetic field Ais differentiable and its exterior derivative corresponding to the magnetic field dAis bounded. In particular, we prove ...

2020

Generating Sparse Stochastic Processes Using Matched Splines

Michaël Unser, Shayan Aziznejad, Leello Tadesse Dadi

We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by Levy white noises. A recent paper showed that these processes are limits in law of generalized compound-P ...

2020