Results 41 to 50 of about 72,702 (264)

Some classical multiple orthogonal polynomials

Journal of Computational and Applied Mathematics, 2001
Recently there has been a renewed interest in an extension of the notion of orthogonal polynomials known as multiple orthogonal polynomials. This notion comes from simultaneous rational approximation (Hermite-Pade approximation) of a system of several functions.
Assche, Walter Van, Coussement, Els
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Discrete Entropies of Chebyshev Polynomials

Mathematics
Because of its flexibility and multiple meanings, the concept of information entropy in its continuous or discrete form has proven to be very relevant in numerous scientific branches. For example, it is used as a measure of disorder in thermodynamics, as
Răzvan-Cornel Sfetcu, Sorina-Cezarina Sfetcu, Vasile Preda   +2 more
doaj   +1 more source

Asymptotic zero distribution of Jacobi-Pi\~neiro and multiple Laguerre polynomials

, 2016
We give the asymptotic distribution of the zeros of Jacobi-Pi\~neiro polynomials and multiple Laguerre polynomials of the first kind. We use the nearest neighbor recurrence relations for these polynomials and a recent result on the ratio asymptotics of ...
Neuschel, Thorsten, Van Assche, Walter
core   +1 more source

Average Characteristic Polynomials of Determinantal Point Processes [PDF]

, 2015
We investigate the average characteristic polynomial $\mathbb E\big[\prod_{i=1}^N(z-x_i)\big] $ where the $x_i$'s are real random variables which form a determinantal point process associated to a bounded projection operator.
Hardy, Adrien
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Computing recurrence coefficients of multiple orthogonal polynomials

, 2015
Multiple orthogonal polynomials satisfy a number of recurrence relations, in particular there is a $(r+2)$-term recurrence relation connecting the type II multiple orthogonal polynomials near the diagonal (the so-called step-line recurrence relation) and
Filipuk, Galina, Haneczok, Maciej, Van Assche, Walter   +2 more
core   +1 more source

Legendre Cooperative PSO Strategies for Trajectory Optimization

Complexity, 2018
Particle swarm optimization (PSO) is a population-based stochastic optimization technique in a smooth search space. However, in a category of trajectory optimization problem with arbitrary final time and multiple control variables, the smoothness of ...
Lei Liu, Yongji Wang, Fuqiang Xie, Jiashi Gao   +3 more
doaj   +1 more source

Analyzing genotype-by-environment interaction using curvilinear regression

Scientia Agricola, 2012
In the context of multi-environment trials, where a series of experiments is conducted across different environmental conditions, the analysis of the structure of genotype-by-environment interaction is an important topic.
Dulce Gamito Santinhos Pereira, Paulo Canas Rodrigues, Iwona Mejza, Stanislaw Mejza, João Tiago Mexia   +4 more
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Polynomials with Odd Orthogonal Multiplicity

Finite Fields and Their Applications, 1998
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SOME RECURRENCE RELATIONS OF MULTIPLE ORTHOGONAL POLYNOMIALS [PDF]

Journal of the Korean Mathematical Society, 2005
Multiple orthogonal polynomial systems (OPS) are considered. A sequence of polynomial vectors \(\{(A_{(n_1,n_2)}, B_{(n_1,n_2)})\}\) is called a multiple OPS of type I relative to a pair of measures \((d\mu,d\nu)\) if (i) \(\deg A_{(n_1,n_2)}=n_1\) and \(\deg B_{(n_1,n_2)}=n_2\); (ii) \(\int_{\mathbb R}x^k (A_{(n_1,n_2)}\, d\mu+ B_{(n_1,n_2)}\,d\nu)=0\)
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Christoffel functions for multiple orthogonal polynomials

Journal of Approximation Theory, 2022
We study weak asymptotic behaviour of the Christoffel--Darboux kernel on the main diagonal corresponding to multiple orthogonal polynomials. We show that under some hypotheses the weak limit of $\tfrac{1}{n} K_n(x,x)\, dμ$ is the same as the limit of the normalized zero counting measure of type II multiple orthogonal polynomials.
Swiderski, Grzegorz, Van Assche, Walter
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