Computation of the modified strong uniqueness constants
Charles B. Dunham, Chang Zhongzhu · International Journal of Computer Mathematics · 1994
Paralleling the classical strong uniqueness, in this paper we consider the modified strong uniqueness which measures the distance between the best approximation and the achieved approximation in the parameter norm instead of uniform (function) norm in which the classical strong uniqueness measures the distance. We introduce a quantity called modified strong uniqueness constant which can be used to bound the distance mentioned above (if we can bound the difference between the minimal approximation error norm and the achieved approximation error norm), and deduce a computation formula for it for both linear and nonlinear uniform approximations. Cline's arguments for the classical strong uniqueness constant are used, but we make some modifications due to the turning of our attention from uniform (function) norm to parameter norm. Implementation of the computation, and examples for computing both classical and modified strong uniqueness constants are given. We also introduce a quantity which is analogous to Lipschitz constant.