Least-squares orthogonal polynomials
Let \(c\) be a linear functional defined on the space of complex polynomials. While orthogonal polynomials \(P_ k\) are defined by \(c(x^ i P_ k(x))=0\) for \(i=1,2,\dots,k-1\), the authors consider polynomials \(R_ k\) which minimize \(\sum_{i=0}^ m [c(x^ i R_ k(x))]^ 2\) and call them least squares orthogonal polynomials. A computation of the polynomials by a Lanczos-type process is considered. The authors discuss how a breakdown of the recursion can be avoided. An application deals with Padé-type approximation.
scientific article; zbMATH DE number 219123