Publications related to Trigonometric interpolation

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in orthologic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based pro ...

Springer International Publishing Ag2024

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in ortho- logic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based p ...

2024

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Volkan Cevher, Thomas Michaelsen Pethick, Wanyun Xie

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

2023

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

Alfio Quarteroni, Francesco Regazzoni

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

Elsevier Science Sa2023

Computer-assisted proof of kernel inequalities

Maryna Viazovska, Abhinav Kumar

This data set provides a computer-assisted proof for the kernel inequalities needed to prove universal optimality in the paper "Universal optimality of the E_8 and Leech lattices and interpolation formulas" (by Cohn, Kumar, Miller, Radchenko, and Viazovska ...

EPFL Infoscience2023

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

Axel Elie Joseph Séguin

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

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Martin Peter Stoller, Joao Pedro Gonçalves Ramos

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

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Martin Vetterli, Paul Hurley, Eric Bezzam, Sepand Kashani, Matthieu Martin Jean-André Simeoni

Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a more natural choi ...

SIAM2022

Fourier Interpolation From Spheres

Martin Peter Stoller

In every dimension d >= 2, we give an explicit formula that expresses the values of any Schwartz function on R-d only in terms of its restrictions, and the restrictions of its Fourier transform, to all origin-centered spheres whose radius is the square roo ...

2021

On Linear Interpolation in the Latent Space of Deep Generative Models

Quentin Christian Becker, Mike Yan Michelis

The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in lat ...

2021

Fourier uniqueness in even dimensions

Maryna Viazovska

In recent work, methods from the theory of modular forms were used to obtain Fourier uniqueness results in several key dimensions (d = 1, 8, 24), in which a function could be uniquely reconstructed from the values of it and its Fourier transform on a discr ...

National Academy of Sciences2021

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

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

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

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

Integrating the Finite Element Method with a Data-Driven Approach for Dam Displacement Prediction

Zhenzhu Meng, Yating Hu, Chenfei Shao

Both numerical simulations and data-driven methods have been applied in dam's displacement modeling. For monitored displacement data-driven methods, the physical mechanism and structural correlations were rarely discussed. In order to take the spatial and ...

2020

Analysis of Resonances in Periodic Metasurfaces through the Concept of Self-Coupling Mode

Kévin Müller

The concept of self-coupling modes, which are eigen-vectors of the roundtrip matrix, is introduced. I investigate its use for the identification and analysis of the resonances taking place in periodic metasurfaces. It also improves the interpolation of the ...

IEEE2019

Fourier interpolation on the real line

Maryna Viazovska

In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set {0,+/- 1,+/- ...

2019

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