Parametric PGD model used with orthogonal polynomials to assess efficiently the building's envelope thermal performance

Orthogonal Polynomials with Orthogonal Derivatives

Deim-based Pgd for Parametric Nonlinear Model Order Reduction

Abstract. A new technique for efficiently solving parametric nonlinear reduced order models in the Proper Generalized Decomposition (PGD) framework is presented here. This technique is based on the Discrete Empirical Interpolation Method (DEIM)[1], and thus the nonlinear term is interpolated using the reduced basis instead of being fully evaluated. The DEIM has already been demonstrated to prov...

Orthogonal Symmetric Polynomials Associated with the Calogero Model

Abstract. The Calogero model is a one-dimensional quantum integrable system with inverse-square long-range interactions confined in an external harmonic well. It shares the same algebraic structure with the Sutherland model, which is also a one-dimensional quantum integrable system with inverse-sine-square interactions. Inspired by the Rodrigues formula for the Jack polynomials, which form the ...

Connection Coefficients of Orthogonal Polynomials with Applications to Classical Orthogonal Polynomials

New criteria for nonnegativity of connection coefficients between to systems of orthogonal polynomials are given. The results apply to classical orthogonal polynomials.

Symmetric Orthogonal Polynomials and the Associated Orthogonal L-polynomials

We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained. Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx2)(l x2)~1/2, k>0.