Convergence Rate Analysis and Improved Iterations for Numerical Radius Computation

The current two main methods for computing the numerical are level-set approach of Mengi and Overton cutting-plane method Uhlig, but until now, no formal convergence rate results have been established either. In practice, which is faster also unclear, with Uhlig's sometimes being much than Overton's approach, on other problems, slower. this paper, we clarify issue propose three improved methods. We show that converges quadratically, as has suspected, while completely characterize total cost so-called disk matrices. Then, arbitrary fields values, derive exact Q-linear local cutting procedure. Together, establishes extremely expensive when field values a centered at origin, his procedure actually varies from linear to superlinear depending shape location can be encapsulated by single parameter via introducing notion normalized curvature. These fully explain why both exceptionally fast slow. With insight, an method, significantly their earlier counterparts, establishing analogous both. Moreover, in order remain efficient any configuration, introduce third algorithm leverages concept curvature combines our iterations.