Modeling the Log Density Distribution with Orthogonal Polynomials

Orthogonal Dirichlet polynomials with arctangent density

Let {λj}∞j=1 be a strictly increasing sequence of positive numbers with λ1 = 1. We find a simple explicit formula for the orthogonal Dirchlet polynomials {φn} formed from linear combinations of { λ j n j=1 , associated with the arctangent density. Thus ∫ ∞ −∞ φn (t)φm (t) dt π (1 + t2) = δmn. We obtain formulae for their Christoffel functions, and deduce their asymptotics, as well as universali...

Orthogonal Polynomials with Orthogonal Derivatives

Modeling agent decisions with a family of orthogonal polynomials

Agents in a multiagent system (MAS) can bene-t by modeling other agents in their environment. In particular, being able to predict decisions to be taken by other agents enables an agent to improve its own utility. In this paper, we present a learning mechanism by which an agent can approximately model the decision function used by another agent given a collection of decisions made by that agent...

Orthogonal polynomials on the unit circle: distribution of zeros

Marcellan, F. and E. Godoy, Orthogonal polynomials on the unit circle: distribution of zeros, Journal of Computational and Applied Mathematics 37 (1991) 195-208. In this paper we summarize some results concerning zeros of orthogonal polynomials with respect to an indefinite inner product. We analyze the inverse problem, i.e., a discrete representation for the functional in terms of the n th ort...

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.