Publications related to Interpolatory Rational Model Order Reduction of Parametric Problems Lacking Uniform Inf-Sup Stability

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Martin Vetterli, Arash Amini, Mitra Fatemi

We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of

\mathds{1}_{\{p\leq0\}}

to the image plane, where

\mathds{1}

denotes the indicator function and

p

is some r ...

2016

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...

2015

Estimation in Functional Lagged Regression

Lukasz Kidzinski

The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-2 in applications. A spectral approach to the estima ...

Wiley-Blackwell2015

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

Giovanni Migliorati

We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is ...

Elsevier2015

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate func- tions based on random sampling according to a given probability measure. Recent work has shown th ...

MATHICSE2014

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

2014

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

Christophe-Aschkan Mery

This project offers a rigorous introduction to the tools needed to construct a continuous stochastic process. Among other things, we give a very detailed proof of the Kolmogorov continuity criterion. We then construct a Brownian Motion following the formal ...

EPFL2013

New Results in the Theory of Linear and Integer Programming

Nicolai Hähnle

The polynomial Hirsch conjecture states that the vertex-edge diameter of a d-dimensional polyhedron with n facets is bounded by a polynomial in d and n. For the special case where the polyhedron is defined as the set of points satisfying a system Ax ≤ b of ...

EPFL2012

Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni, Toni Mikael Lassila

The set of solutions of a parameter-dependent linear partial differential equation with smooth coefficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for ...

Springer2012

MATHICSE Technical Report : Analysis of the discrete $L^2$ projection on polynomial spaces with random evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

MATHICSE2011

Interpolatory Rational Model Order Reduction of Parametric Problems Lacking Uniform Inf-Sup Stability

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Sampling and Reconstruction of Shapes with Algebraic Boundaries

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Estimation in Functional Lagged Regression

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

New Results in the Theory of Linear and Integer Programming

Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs

MATHICSE Technical Report : Analysis of the discrete $L^2$ projection on polynomial spaces with random evaluations

Estimation in Functional Lagged Regression

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

MATHICSE Technical Report : Analysis of the discrete $L^2$ projection on polynomial spaces with random evaluations

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

New Results in the Theory of Linear and Integer Programming

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION