We develop a toolbox for the error analysis of linear recurrences with constant or polynomial coefficients, based on generating series, Cauchy's method of majorants, and simple results from analytic combinatorics. We illustrate the power of the approach by several nontrivial application examples. Among these examples are a new worst-case analysis of an algorithm for computing Bernoulli numbers, and a new algorithm for evaluating differentially finite functions in interval arithmetic while… Expand

This book gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic by combining algorithmic derivations, perturbation theory, and rounding error analysis.Expand

Thank you very much for reading ordinary differential equations in the complex domain, maybe you have knowledge that, people have look hundreds of times for their chosen readings like this, but end up in infectious downloads.Expand

This paper is concerned with the numerical solution of the general initial value problem for linear recurrence relations. An error analysis of direct recursion is given, based on relative rather than… Expand

In this paper, we study the stability of certain computational algorithms associated with second order difference equations. The methods are based on the forward use of the difference equation, and… Expand