Publications related to Homogeneous polynomial

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

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 : 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 sa ...

MATHICSE2015

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 : INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutations 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 ...

MATHICSE2015

Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation

Alfio Quarteroni, Luca Dede', Christoph Jäggli

In this paper, we carry out a numerical dispersion analysis for the linear two-dimensional elastodynamics equations approximated by means of NURBS-based Isogeometric Analysis in the framework of the Galerkin method; specifically, we consider the analysis o ...

Elsevier2015

Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry

Pramod Rastogi, Rishikesh Dilip Kulkarni

A novel technique is proposed for the simultaneous measurement of all three components of displacement from a single recording of the interference field in digital holographic interferometry. The interference field is divided into a number of rectangular s ...

Optical Soc Amer2015

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

Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

2014

Homogeneous number of free generators

We address two questions of Simon Thomas. First, we show that for any n >= 3 one can find a four-generated free subgroup of SLn (Z) which is profinitely dense. More generally, we show that an arithmetic group Gamma that admits the congruence subgroup prope ...

Walter De Gruyter Gmbh2014

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

Homogeneous polynomial

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

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

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

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

Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation

Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Perturbation analysis for the Darcy problem with log-normal permeability

Homogeneous number of free generators

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

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

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation

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

Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry

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

Perturbation analysis for the Darcy problem with log-normal permeability

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

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Homogeneous number of free generators