COMPUTATION OF THE MODIFIED STRONG UNIQUENESS CONSTANTS

Paralleling the classical strong uniqueness, in this paper we consider the modified strong uniqueness which measures the distance between th e best approximation and the achieved approximation in the parameter n orm instead of uniform (function) norm in which the classical strong u niqueness measures the distance. We introduce a quantity called modifi ed strong uniqueness constant which can be used to bound the distance mentioned above (if we can bound the difference between the minimal ap proximation error norm and the achieved approximation error norm), and deduce a computation formula for it for both linear and nonlinear uni form approximations. Cline's arguments for the classical strong unique ness constant are used, but we make some modifications due to the turn ing of our attention from uniform (function) norm to parameter norm. I mplementation of the computation, and examples for computing both clas sical and modified strong uniqueness constants are given. We also intr oduce a quantity which is analogous to Lipschitz constant.