Root Finding With Interval Arithmetic

TL;DR

This paper discusses the use of interval arithmetic for solving nonlinear equations in one variable, emphasizing the simplicity of single-variable problems and providing a C++ implementation.

Contribution

It offers a focused analysis of interval arithmetic methods for root finding in one variable and shares an open-source implementation.

Findings

Interval arithmetic simplifies single-variable root finding.

Specific methods are more effective for one-variable problems.

Open-source C++ code is provided for practical use.

Abstract

We consider the solution of nonlinear equations in one real variable, the problem usually called by root finding. Although this is an old problem, we believe that some aspects of its solution using interval arithmetic are not well understood, and we present our views on this subject. We argue that problems with just one variable are much simpler than problems with more variables, and we should use specific methods for them. We provide an implementation of our ideas in C++, and make this code available under the Mozilla Public License 2.0.