An optimal sequential algorithm for the uniform approximation of convex functions on [0,1]2
Copyright policy )An optimal sequential algorithm for the uniform approximation of convex functions on [0,1]2
In this paper an algorithm is given for the sequential selection ofN nodes (i.e., measurement points) for the uniform approximation (recovery) of convex functions over [0, 1]2, which has almost optimal order global error, (źc1Nź1lgN), over a naturally defined class of convex functions. This shows the essential superiority of sequential algorithms for this class of approximation problems because any simultaneous choice ofN nodes leads to a global error >c0Nź1/2. New construction and estimation methods are presented, with possible (e.g., multidimensional) generalizations.
- Eötvös Loránd University Hungary
global error, lower bounds, Algorithms for approximation of functions, error estimates, sequential algorithm for the uniform approximation of convex functions, Multidimensional problems, Rate of convergence, degree of approximation, sequential selection of nodes for uniform approximation of convex functions, Approximation by other special function classes
global error, lower bounds, Algorithms for approximation of functions, error estimates, sequential algorithm for the uniform approximation of convex functions, Multidimensional problems, Rate of convergence, degree of approximation, sequential selection of nodes for uniform approximation of convex functions, Approximation by other special function classes
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