HSbound
HSbound is a mathematical construct used in analysis and applied disciplines to denote a bound on a quantity of interest that depends on two core components denoted as HS: a measure of smoothness or sparsity and a scale parameter representing the size or resolution of the problem. The purpose of an HSbound is to provide a computable upper limit under a prescribed set of assumptions, enabling comparisons across methods and settings.
Definition and scope. An HSbound typically bounds either an error term or a probability, given assumptions
Computation. In practice, HSbound is derived by combining standard inequalities with problem-specific information. Common tools include
Applications. HSbound appears in numerical analysis to bound discretization or approximation errors, in statistics to bound
History and variants. Various variants of HSbound exist, adapted to particular domains or risk measures. Related