Mathematics > Numerical Analysis
arXiv:2606.14467 (math)
[Submitted on 12 Jun 2026]
Abstract:In 2002, V. N. Temlyakov established a criterion for the convergence of the weak greedy algorithm in a Hilbert space for a given weakness sequence $ \tau = \{t_1,t_2,\ldots\} $. The criterion requires verifying a certain limiting relation for every nonnegative square-summable sequence. We give an equivalent closed-form criterion: the weak greedy algorithm converges if and only if $ \sum_{n=1}^{\infty}(1+ n\sum_{k=1}^{n}t_k^2 )^{-1/2}t_n^2=+\infty $.
Submission history
From: Mikhail Novikov [view email]
[v1]
Fri, 12 Jun 2026 14:00:03 UTC (14 KB)
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