Publications related to Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

MATHICSE Technical Report : Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

We study the Darcy boundary value problem with log-normal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the stochastic solu ...

MATHICSE2020

Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Fabio Nobile, Francesca Bonizzoni

We study the Darcy boundary value problem with lognormal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the stochastic solut ...

2020

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

Ali H. Sayed, Stefan Vlaski

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In this work we establish that agents cluster around a network centroid in the mean-fourth sen ...

IEEE2019

MATHICSE Technical Report: Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability

Davide Pradovera

We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR stategy co ...

MATHICSE2019

Stable high-order randomized cubature formulae in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

2018

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Damian Mateusz Straszak

Optimization is a fundamental tool in modern science. Numerous important tasks in biology, economy, physics and computer science can be cast as optimization problems. Consider the example of machine learning: recent advances have shown that even the most s ...

EPFL2018

Sampling at unknown locations, with an application in surface retrieval

Martin Vetterli, Benjamin Bejar Haro, Adam James Scholefield, Michalina Wanda Pacholska

We consider the problem of sampling at unknown locations. We prove that, in this setting, if we take arbitrarily many samples of a polynomial or real bandlimited signal, it is possible to find another function in the same class, arbitrarily far away from t ...

2017

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function

u

in multivariate polynomial spaces

P_\Lambda:=span\{y\mapsto y^\nu \,: \, \nu\in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma:=[-1,1]^d

, based on the s ...

2017

MATHICSE Technical Report : Multilevel weighted least squares polynomial approximation

Fabio Nobile

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...

MATHICSE2017

Multilevel weighted least squares polynomial approximation

Fabio Nobile

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...

2017

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

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MATHICSE Technical Report : Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

MATHICSE Technical Report: Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability

Stable high-order randomized cubature formulae in arbitrary dimension

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Sampling at unknown locations, with an application in surface retrieval

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

MATHICSE Technical Report : Multilevel weighted least squares polynomial approximation

Multilevel weighted least squares polynomial approximation

Sampling at unknown locations, with an application in surface retrieval

MATHICSE Technical Report : Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

Stable high-order randomized cubature formulae in arbitrary dimension

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

MATHICSE Technical Report: Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

MATHICSE Technical Report : Multilevel weighted least squares polynomial approximation

Multilevel weighted least squares polynomial approximation