Vector orthogonal polynomials

Vector Orthogonal Polynomials and Least Squares Approximation

We describe an algorithm for complex discrete least squares approximation, which turns out to be very efficient when function values are prescribed in points on the real axis or on the unit circle. In the case of polynomial approximation, this reduces to algorithms proposed by Rutishauser, Gragg, Harrod, Reichel, Ammar and others. The underlying reason for efficiency is the existence of a recur...

Vector Orthogonal Polynomials of Dimension ?d

Vector orthogonal polynomials of dimension ?d where d is a nonzero positive integer are deened. They are proved to satisfy a recurrence relation with d + 2 terms. A Shohat{Favard type theorem and a QD like algorithm are given.

Frequency domain identification of multivariable systems using vector orthogonal polynomials

Frequency domain methods are known to suffer from a poor numerical conditioning when the frequency span and/or the model order become large (more than two decades and an order larger than twenty). This numerical problem destroys both the modeling performance and the model order selection capability. This paper presents a modeling approach that leads to (almost) optimal numerical conditioning of...

Orthogonal Polynomials

The theory of orthogonal polynomials plays an important role in many branches of mathematics, such as approximation theory (best approximation, interpolation, quadrature), special functions, continued fractions, differential and integral equations. The notion of orthogonality originated from the theory of continued fractions, but later became an independent (and possibly more important) discipl...

Orthogonal Polynomials