On the stability of interval decomposable persistence modules
The authors focus on the classical algebraic stability theorem for persistence modules which is a central result in the theory of stability for persistent homology. In particular they prove that \[d_B(\mathcal{B}(M), \mathcal{B}(N)) \leq (2n - 1)d_I (M, N ), \] for rectangle decomposable \(\mathbb{R}^n\)-modules. That \[d_B(\mathcal{B}(M), \mathcal{B}(N)) \leq (n - 1)d_I (M, N ), \] for free \(\mathbb{R}^n\)-modules, and finally that equality holds for block decomposable modules.
scientific article; zbMATH DE number 7367365
scientific article