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-1 $begingroup$ Is it true that $forall lambda>0$ $$lim_{ntoinfty}frac{sum_{i=1}^ni^{4lambda}}{Big(sum_{i=1}^ni^{2lambda}Big)^2}=0$$ I cannot find a way to prove it, nor can I find a counterexample. Any help is greatly appreciated! limits sums-of-squares gauss-sums share | cite | improve this question asked Dec 15 '18 at 15:07 newbie newbie 313 2 12 $endgroup$ 4

0 $begingroup$ I have a sparse representation problem where I have the linear model $ mathbf{x} approx DA $ , where $D$ $in$ $mathbb{R}^{N times K}$ is the dictionary I want to learn and $A=[alpha_{1}, ..., alpha_{M}]$ $in$ $mathbb{R}^{K times M}$ is a matrix of representations of x $in$ $mathbb{R}^{N times M}$ . x is the observation data with sparsity level $L$ (means that $|| mathbf{x}||_{0} leq L)$ . We have an underdetermined system which means that $N<K$ . What is the absolute requirement of samples (how big does $M$ have to be) in order to be able to learn $D$ ? machine-learning sparse-matrices share | cite | improve this question