Introduction to Reliable Computing
Alfredo Vaccaro · 2023
The power system research community started adopting reliable computing-based models, which allow the accuracy of the computed quantities to be automatically estimated as part of the process of computing them. Interval analysis (IA) is a range-based model for numerical computing. The interval extensions of the main mathematical operators and elementary functions can be composed in order to compute the interval extensions for any complex function by using the same mathematical schemes adopted in real numbers computing. The interval-based arithmetic operators generalize the arithmetic of real numbers to the set of real intervals. An useful application of IA-based computing is in computing reliable interval enclosures of the solution sets of uncertain nonlinear equations. It is possible to properly integrate affine arithmetic (AA) and IA-based computing, in order to try and get the best out of the two techniques, namely to use IA for reducing the overestimation of nonaffine operations, and AA.