A Dataset of Nonlinear Equations for Subdivision

Abstract

In this paper, we report on the largest labelled dataset constructed so far for solving zero-dimensional square nonlinear systems with subdivision-based methods. A brief, non-exhaustive survey with emphasis on the literature from the past two decades is also provided to accompany with the dataset. The value of the dataset has been demonstrated through benchmarking several solvers as well as being used for learning to classify the real roots of nonlinear parametric systems.

Figures (11)

• Figure 1: Forward (left) and backward (right) propagation for the constraint $2^x=z+y^2$.
• Figure 2: The box $([-1,1],[-1,1])$ is hull consistent and box consistent with respect to the system $\{x_2=-x_1, 2x_2=(x_1+1)^2-2\}$.
• Figure 3: Multi-joint robot arm.
• Figure 4: A Stewart platform.
• Figure 5: Geometric setup: the points $P_i$ mark observer positions, and the lines depict the observed lines of sight.