Greedy Approximation in Certain Subsystems of the Schauder System
M. G. Grigoryan, A. A. Sargsyan, and R. E. Zink
Source: Real Anal. Exchange Volume 34, Number 1 (2008), 227-238.
Abstract
Although the sequence of greedy approximants associated with the Schauder expansion of a function, $f$, continuous on $[0,1]$, may fail to converge, there always will be a continuous function, arbitrarily close to $f$, whose Schauder expansion does have a convergent sequence of greedy approximants. Further examination of this problem shows that the same sort of proposition is valid for a multitude of subsystems of the Schauder system.
Primary Subjects: 42C10
Keywords: greedy algorithm ; Schauder expansion
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