Exclusion regions for parameter-dependent systems of equations

Abstract This paper presents a new algorithm based on interval methods for rigorously constructing inner estimates of feasible parameter regions together with enclosures the solution set parameter-dependent systems nonlinear equations in low (parameter) dimensions. The proposed method allows to explicitly construct sets around regular value, and enclose particular curve (resp. manifold) by union inclusion regions, simultaneously. is calculation exclusion zeros square equations. Starting from an approximate at fixed p parameters, provides algorithmic concept how box $${\mathbf {s}}$$ s such that each element $$s\in {\mathbf ∈ existence can be proved within certain error bounds.