rootslikely

RootsLikely is a lightweight, open source statistical library designed to estimate the probability distribution of the roots of nonlinear equations in one dimension. It was introduced in 2023 by the mathematical software group at the University of Lisbon. The primary goal of RootsLikely is to provide practitioners in applied mathematics, engineering, and finance with tools to quantify uncertainty in root-finding problems that arise when input data is noisy or when the equation contains stochastic parameters.

The core algorithm combines a Monte Carlo sampling of parameter space with a Newton‑Raphson iteration to locate candidate roots. For each sampled instance the algorithm records the iteration path, allowing users to construct an empirical cumulative distribution function for the root location. RootsLikely supports both deterministic and stochastic function definitions, and can be integrated with common numerical computing environments such as Python’s NumPy and SciPy. The library includes visualization utilities that plot confidence bands around numerical solutions, making it suitable for sensitivity analyses in scientific research.

RootsLikely has been cited in a number of conference proceedings, most notably the 2024 NIPS Workshop on Uncertainty Quantification, where it was demonstrated on problems ranging from logistic regressions with measurement error to model calibration for climate simulations. Future releases aim to extend multivariate support and to incorporate Bayesian inference techniques for higher‑dimensional root-finding tasks.