The convergence rate of the sandwich algorithm for approximating convex functions
Copyright policy )The convergence rate of the sandwich algorithm for approximating convex functions
Interval bisection, slope bisection, maximum error rule and chord rule are considered as four natural rules leading to different versions of the sandwich algorithm for approximating a convex function of one variable over an interval by evaluating the function and its derivative at a sequence of points. Further the author demonstrates that the global approximation error with \(n\) evaluation points decreases by the order of \(O(1/n^ 2)\) which is optimal.
- University of Graz Austria
- Graz University of Technology Austria
slope bisection, convex function, sandwich algorithm, Convexity of real functions in one variable, generalizations, convergence rate, maximum error rule, Algorithms for approximation of functions, Approximation with constraints, interval bisection, chord rule
slope bisection, convex function, sandwich algorithm, Convexity of real functions in one variable, generalizations, convergence rate, maximum error rule, Algorithms for approximation of functions, Approximation with constraints, interval bisection, chord rule
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).53 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 1% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!