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Complete Parametrization of Piecewise-Polynomial Interpolators According to Degree, Support, Regularity, and Order

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Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

Espen Sande

We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...

ELSEVIER SCIENCE SA2022

MATHICSE Technical Report: THU-Splines - Highly Localized Refinement on Smooth Unstructured Splines

Xiaodong Wei

We present a novel method named truncated hierarchical unstructured splines (THU-splines) that supports both local h-refinement and unstructured quadrilateral meshes. In a THU-spline construction, an unstructured quadrilateral mesh is taken as the input co ...

MATHICSE2021

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

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 ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

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

COMPUTATION OF "BEST" INTERPOLANTS IN THE L-p 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 t ...

IEEE2020

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 ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Generating Sparse Stochastic Processes Using Matched Splines

Michaël Unser, Leello Tadesse Dadi, Shayan Aziznejad

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 ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Domain-Informed Spline Interpolation

Dimitri Nestor Alice Van De Ville, Hamid Behjat, Zafer Dogan

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a single homogeneous domain. In contrast, many naturally occurring signals lie on an inhomogeneous domain, such as brain activity associated to different brain ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

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