Concept

Phénomène de Runge

Publications associées (72)

Local Barycentric Coordinates

Barycentric coordinates yield a powerful and yet simple paradigm to interpolate data values on polyhedral domains. They represent interior points of the domain as an affine combination of a set of control points, defining an interpolation scheme for any fu ...

Association for Computing Machinery2014

Can Localization Microscopy Benefit From Approximation Theory?

Michaël Unser, Cédric René Jean Vonesch, Hagay Kirshner

We introduce a general and computationally efficient approach to 3-D localization microscopy. The main idea is to construct a continuous-domain representation of the PSF by expanding it in a polynomial B-spline basis. This allows us to fit the PSF to the d ...

IEEE2013

Characterization of T-splines with reduced continuity order on T-meshes

Annalisa Buffa, Mithlesh Kumar

The use of T-splines [30] in Isogeometric Analysis [24] has been proposed in [5] as a tool to enhance the flexibility of isogeometric methods. If T-splines are a very general concept, their success in isogeometric analysis relies upon some basic properties ...

2012

Accurate reconstruction of discontinuous functions using the singular pade-chebyshev method

Jan Sickmann Hesthaven

In this paper, we present a singularity-based resolution of the Gibbs phenomenon that obstructs the reconstruction of a function with jump discontinuities by a truncated Chebyshev series or a PadÃ©-Chebyshev approximation. We tackle the more difficult case ...

2012

Chebyshev interpolation for nonlinear eigenvalue problems

Daniel Kressner, Peter Cedric Effenberger

This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix-valued function is computationally expensive. ...

Springer Netherlands2012

B-spline goal-oriented error estimators for geometrically nonlinear rods

Luca Dede'

We consider goal-oriented a posteriori error estimators for the evaluation of the errors on quantities of interest associated with the solution of geometrically nonlinear curved elastic rods. For the numerical solution of these nonlinear one-dimensional pr ...

Springer Verlag2012

Reconstruction of Large, Irregularly Sampled Multidimensional Images. A Tensor-Based Approach

Michaël Unser

Many practical applications require the reconstruction of images from irregularly sampled data. The spline formalism offers an attractive framework for solving this problem; the currently available methods, however, are hard to deploy for large-scale inter ...

IEEE2011

Phase estimation in digital holographic interferometry using cubic phase function based method

Pramod Rastogi, Sai Siva Gorthi

The paper introduces a cubic-phase-function based method to estimate interference phase in digital holographic interferometry. The proposed method relies on piecewise polynomial approximation of phase by dividing an arbitrary row/column of the complex reco ...

Taylor & Francis2010

Comparative Analysis of Various Single-tone Frequency Estimation Techniques in High-order Instantaneous Moments Based Phase Estimation Method

Pramod Rastogi, Sai Siva Gorthi

For phase estimation in digital holographic interferometry, a high-order instantaneous moments (HIM) based method was recently developed which relies on piecewise polynomial approximation of phase and subsequent evaluation of the polynomial coefficients us ...

AIP Conf. Proc.2010

Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map

Gianluigi Rozza, Andrea Manzoni, Toni Mikael Lassila

Reduced basis approximations for geometrically parametrized advection- diffusion equations are investigated. The parametric domains are assumed to be images of a reference domain through a piecewise polynomial map; this may lead to nonaffinely parametrized ...

Springer2010

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