Abstract
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 the Bernoulli numbers and a new algorithm for evaluating differentially finite functions in interval arithmetic while avoiding interval blow-up.
| Original language | English |
|---|---|
| Pages (from-to) | 196-227 |
| Number of pages | 32 |
| Journal | Electronic Transactions on Numerical Analysis |
| Volume | 58 |
| DOIs | |
| Publication status | Published - 1 Jan 2023 |
Keywords
- Bernoulli numbers
- complex variable
- differentially finite function
- majorant series
- rigorous computing
- rounding error
- vibrating string