This research introduces a novel computational framework for calculating topological degrees of mappings defined on sets that satisfy relaxed star-shapedness conditions, extending classical topological degree theory to broader classes of non-convex domains.
Key findings
Introduces weakly star-shaped sets and their generalized kernels, extending topological degree theory.
Develops an algorithm for computing the generalized kernel based on sampling and visibility constraints.
Proposes a certified algorithm combining simplicial approximation with interval arithmetic for degree computation.
Establishes theoretical foundations including existence theorems, convergence guarantees, and complexity bounds.
Limitations & open questions
The computational implications of relaxed star-shapedness conditions remain largely unexplored.
The algorithm's practical applicability to high-dimensional problems is not yet established.