2004/07/12 by Alicja Smoktunowicz, Smoktunowicz, Alicja, Przemysław Kosowski +3
Computer Science · Engineering · Mathematics · #65D05 #65G50 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.math/0407195
openalex publication_date 2004/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The scheme of divided differences is widely used in many approximation and interpolation problems. Computing the Newton coefficients of the interpolating polynomial is the first step of the Björck and Pereyra algorithm for solving Vandermonde systems of equations (Cf. \citebjorck: 70). Very often this algorithm produces very accurate solution. The problem of determining the Newton coefficients is intimately related with the problem of evaluation the Lagrange interpolating polynomial, which can be realized by many algorithms. For these reasons we use the uniform approach and analyze also Aitken's algorithm of the evaluation of an interpolating polynomial. We propose new algorithms that are always numerically stable with respect to perturbation in the function values and more accurate than the Aitken's algorithm and the scheme of divided differences, even for complex data.