Coalescing points for eigenvalues of banded matrices depending on parameters with application to banded random matrix functions

@article{Dieci2018CoalescingPF,
  title={Coalescing points for eigenvalues of banded matrices depending on parameters with application to banded random matrix functions},
  author={Luca Dieci and Alessandra Papini and Alessandro Pugliese},
  journal={Numerical Algorithms},
  year={2018},
  volume={80},
  pages={1241-1266}
}
In this work, we develop and implement new numerical methods to locate generic degeneracies (i.e., isolated parameters’ values where the eigenvalues coalesce) of banded matrix valued functions. More precisely, our specific interest is in two classes of problems: (i) symmetric, banded, functions A(x) ∈ ℝn×n, smoothly depending on parameters x ∈ Ω ⊂ ℝ2 and (ii) Hermitian, banded, functions A(x) ∈ ℂn×n, smoothly depending on parameters x ∈Ω⊂ ℝ3. The computational task of detecting coalescing… CONTINUE READING