Global solver based on the Sperner lemma and Mazurkewicz–Knaster‐Kuratowski–lemma based proof of the Brouwer fixed‐point theorem

Key Points

• The fixed-point solver yields mappings from a simplex into itself, and is proven to be global.
• Using topological arguments, it employs the constructive proof of the Mazurkewicz–Knaster–Kuratowski lemma.
• Analysis focuses on function evaluations that halve the error, ensuring high accuracy during computations.
• The implications support broader applications in mathematical analysis and computational geometry.