Multiple orthogonal polynomials (MOPs) extend the classical notion of orthogonality by satisfying simultaneous orthogonality conditions with respect to several weight functions or measures. This ...

We find necessary and sufficient conditions for a spectral differential equation LN[ y ](x) = ∑N i = 1 ℓi(x)y(i)(x) = λn y(x) to have Sobolev orthogonal polynomials of solutions, which are orthogonal ...

The paper characterizes matrices A = {aij i,j=0 N which have a given system of vectors orthogonal with respect to a given probability distribution as its right eigenvectors. Results of Hoare and ...

We discuss the application of orthogonal polynomials to the estimation of probability density functions, particularly with regard to accessing features of a portfolio's profit/loss distribution. Such ...

Shrinking technology nodes and smaller process margins require improved photolithography overlay control. Generally, overlay measurement results are modeled with Cartesian polynomial functions for ...