Publications related to Homogeneous polynomial

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

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

Combinatorial Penalties: Which structures are preserved by convex relaxations?

Volkan Cevher, Marwa El Halabi

We consider the homogeneous and the non-homogeneous convex relaxations for combinatorial penalty functions defined on support sets. Our study identifies key differences in the tightness of the resulting relaxations through the notion of the lower combinato ...

2017

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

A Semidefinite Programming Approach to Control Synthesis for Stochastic Reach-Avoid Problems

Maryam Kamgarpour, John Lygeros

We propose a computational approach to approximate the value function and control poli- cies for a finite horizon stochastic reach-avoid problem as follows. First, we formulate an infinite dimensional linear program whose solution characterizes the optimal ...

EPiC Series in Computing2017

The Interface Control Domain Decomposition Method For Stokes-Darcy Coupling

Alfio Quarteroni, Marco Discacciati

The interface control domain decomposition (ICDD) method of Discacciati, Gervasio, and Quarteroni [SIAM J. Control Optim., 51 (2013), pp. 3434-3458, doi:10.1137/120890764; J. Coupled Syst. Multiscale Dyn., 1 (2013), pp. 372-392, doi:10.1166/jcsmd.2013.1026 ...

Siam Publications2016

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Frank de Zeeuw

Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...

Duke Univ Press2016

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

INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

Alfio Quarteroni, Simone Deparis, Davide Forti

We are interested in the approximation of partial differential equations on domains decomposed into two (or several) subdomains featuring non-conforming interfaces. The non-conformity may be due to different meshes and/or different polynomial degrees used ...

Elsevier2016

Eigenfunction expansions of ultradifferentiable functions and ultradistributions

Aparajita Dasgupta

In this paper we give a global characterisation of classes of ultradi_erentiable functions and corresponding ultradistributions on a compact manifold X. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on X. Thi ...

2016

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

Homogeneous polynomial

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

Combinatorial Penalties: Which structures are preserved by convex relaxations?

Sampling at unknown locations, with an application in surface retrieval

A Semidefinite Programming Approach to Control Synthesis for Stochastic Reach-Avoid Problems

The Interface Control Domain Decomposition Method For Stokes-Darcy Coupling

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Sampling and Reconstruction of Shapes with Algebraic Boundaries

INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

Eigenfunction expansions of ultradifferentiable functions and ultradistributions

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

Combinatorial Penalties: Which structures are preserved by convex relaxations?

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

Eigenfunction expansions of ultradifferentiable functions and ultradistributions

Sampling at unknown locations, with an application in surface retrieval

Sampling and Reconstruction of Shapes with Algebraic Boundaries

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

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

A Semidefinite Programming Approach to Control Synthesis for Stochastic Reach-Avoid Problems

The Interface Control Domain Decomposition Method For Stokes-Darcy Coupling