An algorithm for the quadratic approximation (Q762703)

Given f, the polynomials \(p\in \Pi_{\ell}\), \(q\in \Pi_ m\), \(r\in \Pi_ n\) are called a quadratic approximation, if \(pf^ 2+qf+r=O(x^{\ell +m+n+2})\). This concept generalizes Padé approximation. Similar recursion formulas for the polynomials are established. Specifically, an analogue of the Mühlbach-Neville-Aitken scheme is discussed. An algorithm in some symbolic language (father: probably FORTRAN, mother:ALGOL) is presented. Numerical results for \(e^ x\) and another function are given.