Publications related to Approximation theory

Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs

In this paper we present some heuristic strategies to compute rapid and reliable approximations to stability factors in nonlinear, inf-sup stable parametrized PDEs. The efficient evaluation of these quantities is crucial for the rapid construction of a pos ...

Springer Verlag2015

MATHICSE Technical Report : IGS: an IsoGeometric approach for Smoothing on surfaces

Luca Dede'

We propose an Isogeometric approach for smoothing on surfaces, namely estimating a function starting from noisy and discrete measurements. More precisely, we aim at estimating functions lying on a surface represented by NURBS, which are geometrical represe ...

MATHICSE2015

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

Fabio Nobile, Giovanni Migliorati

We analyze the stability and accuracy of discrete least squares on multivariate polynomial spaces to approximate a given function depending on a multivariate random variable uniformly distributed on a hypercube. The polynomial approximation is calculated s ...

2015

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

Fabio Nobile, Giovanni Migliorati

We analyze the stability and accuracy of discrete least squares on multivariate poly- nomial spaces to approximate a given function depending on a multivariate random variable uniformly distributed on a hypercube. The polynomial approximation is calculated ...

MATHICSE2015

MATHICSE Technical Report : Convergence of quasi-optimal sparse grid approximation of Hilbert-valued functions: application to random elliptic PDEs

Fabio Nobile, Lorenzo Tamellini

In this work we provide a convergence analysis for the quasi-optimal version of the Stochastic Sparse Grid Collocation method we had presented in our previous work \On the optimal polynomial approximation of Stochastic PDEs by Galerkin and Collocation meth ...

MATHICSE2014

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Michaël Unser, Virginie Sophie Uhlmann

Cardinal Hermite exponential spline functions are a generalization of the classical cardinal Hermite polynomial splines. In this work we consider the 4-dimensional space

ε _{ 4 }

= {1, x,

e ^{ \alpha x }

,

e ^{ -\alpha x }

} with α ∈ $ ℝ ^{ + } ...

SMAI-SIGMA2014

Bounding the Polynomial Approximation Errors of Frequency Response Functions

Zlatko Emedi

Frequency response function (FRF) measurements take a central place in the instrumentation and measurement field because many measurement problems boil down to the characterization of a linear dynamic behavior. The major problems to be faced are leakage an ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Bounding the Polynomial Approximation Errors of Frequency Response Functions

Zlatko Emedi

Frequency response function (FRF) measurements take a central place in the instrumentation and measurement field because many measurement problems boil down to the character- ization of a linear dynamic behavior. The major problems to be faced are leakage ...

Ieee-Inst Electrical Electronics Engineers Inc2013

On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods

Fabio Nobile, Lorenzo Tamellini

In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by mu ...

World Scientific Publ Co Pte Ltd2012

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

Approximation theory

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Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs

MATHICSE Technical Report : IGS: an IsoGeometric approach for Smoothing on surfaces

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

MATHICSE Technical Report : Convergence of quasi-optimal sparse grid approximation of Hilbert-valued functions: application to random elliptic PDEs

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Bounding the Polynomial Approximation Errors of Frequency Response Functions

Bounding the Polynomial Approximation Errors of Frequency Response Functions

On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods

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

MATHICSE Technical Report : IGS: an IsoGeometric approach for Smoothing on surfaces

Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

Bounding the Polynomial Approximation Errors of Frequency Response Functions

Bounding the Polynomial Approximation Errors of Frequency Response Functions

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

MATHICSE Technical Report : Convergence of quasi-optimal sparse grid approximation of Hilbert-valued functions: application to random elliptic PDEs

On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods

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