Concept

Monomial basis

Related publications (32)

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

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

Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis

Daniel Kressner

Novel memory-efficient Arnoldi algorithms for solving matrix polynomial eigenvalue problems are presented. More specifically, we consider the case of matrix polynomials expressed in the Chebyshev basis, which is often numerically more appropriate than the ...

Wiley-Blackwell2014

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

Silvia Sabatini

In [GT], Goldin and Tolman extend some ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. (See also [Kn99,Kn08].) The main goal of this paper is to build on this ...

Int Press Boston, Inc2013

Approximate dynamic programming via sum of squares programming

Maryam Kamgarpour, Tyler Summers

We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision variables. By rela ...

2013

A common theory for phase-modulated homonuclear decoupling in solid-state NMR

David Lyndon Emsley

We propose a new framework for homonuclear dipolar decoupling in solid-state NMR that provides a theoretical link between the FSLG, PMLG and DUMBO families. We show that through the use of a Legendre polynomial basis, the phase modulation of these decoupli ...

ROYAL SOC CHEMISTRY2012

ElimLin Algorithm Revisited

Serge Vaudenay, Pouyan Sepehrdad, Petr Susil

ElimLin is a simple algorithm for solving polynomial systems of multivariate equations over small finite fields. It was initially proposed as a single tool by Courtois to attack DES. It can reveal some hidden linear equations existing in the ideal generate ...

Springer2012

Chebyshev interpolation for nonlinear eigenvalue problems

Daniel Kressner, Peter Cedric Effenberger

This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix-valued function is computationally expensive. ...

Springer Netherlands2012

High order methods for the approximation of the incompressible Navier-Stokes equations in a moving domain

Alfio Quarteroni, Gonçalo Pena

In this paper we address the numerical approximation of the incompressible Navier-Stokes equations in a moving domain by the spectral element method and high order time integrators. We present the Arbitrary Lagrangian Eulerian (ALE) formulation of the inco ...

Elsevier2012

Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients

Fabio Nobile, Lorenzo Tamellini

In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence ...

2011

Analysis of energy savings potentials for integrated room automation

Colin Neil Jones

The energy savings potential of selected low-cost measures related to the simultaneous control of blinds, electric lighting, heating, cooling and ventilation in a single building zone (Integrated Room Automation) was investigated. The analysis was based on ...

2010

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