Publications related to Resultant

Formal Verification of Integer Multipliers by Combining Gröbner Basis with Logic Reduction

Formal verification utilizing symbolic computer algebra has demonstrated the ability to formally verify large Galois field arithmetic circuits and basic architectures of integer arithmetic circuits. The technique models the circuit as Gröbner basis polynom ...

IEEE2016

Innovative photo-Fenton catalysis by PE-FeOx films leading to methylene blue (MB) degradation: Kinetics, surface properties and mechanism

César Pulgarin, Juan Kiwi, Rosendo Sanjines, Laura Victoria Suárez Murillo, Huiyu Dong

This study reports an innovative preparation polyethylene-FeOx (PE-FeOx films) leading to the degradation of the methylene blue (MB) dye under low intensity sunlight/visible light (>400 nm). The intermediate highly oxidative radicals generated by PE-FeOx l ...

Elsevier2016

Shapes from Pixels

Mitra Fatemi

In today's digital world, sampling is at the heart of any signal acquisition device. Imaging devices are ubiquitous examples that capture two-dimensional visual signals and store them as the pixels of discrete images. The main concern is whether and how th ...

EPFL2016

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

On the discrete logarithm problem in finite fields of fixed characteristic

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For

q

a prime power, the discrete logarithm problem (DLP) in

\mathbb{F}_q

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer

x

such that

g^x = h

. We present an algorithm for computing discrete log ...

2015

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

Interactive real-time physics: An intuitive approach to form-finding and structural analysis for design and education

Gennaro Senatore

Real-time physics simulation has been extensively used in computer games, but its potential has yet to be fully realized in design and education. We present an interactive 3D physics engine with a wide variety of applications. In common with traditional FE ...

2015

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

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

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Formal Verification of Integer Multipliers by Combining Gröbner Basis with Logic Reduction

Innovative photo-Fenton catalysis by PE-FeOx films leading to methylene blue (MB) degradation: Kinetics, surface properties and mechanism

Shapes from Pixels

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

On the discrete logarithm problem in finite fields of fixed characteristic

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

Interactive real-time physics: An intuitive approach to form-finding and structural analysis for design and education

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

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

Shapes from Pixels

Formal Verification of Integer Multipliers by Combining Gröbner Basis with Logic Reduction

On the discrete logarithm problem in finite fields of fixed characteristic

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

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

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

Interactive real-time physics: An intuitive approach to form-finding and structural analysis for design and education

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

Innovative photo-Fenton catalysis by PE-FeOx films leading to methylene blue (MB) degradation: Kinetics, surface properties and mechanism