Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Greedy algorithms and M-term approximation with regard to redundant dictionaries
Journal of Approximation Theory
Approximation of functions over redundant dictionaries using coherence
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On Lebesgue-type inequalities for greedy approximation
Journal of Approximation Theory
Algorithms for subset selection in linear regression
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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Given a redundant dictionary @F, represented by an MxN matrix (@F@?R^M^x^N) and a target signal y@?R^M, the sparse approximation problem asks to find an approximate representation of y using a linear combination of at most k atoms. This note presents a hardness result for sparse approximation problem under a measure of quality, which is essentially the squared multiple correlation in statistical analysis. We show that unless P=NP, all polynomial time algorithms which provide a k-sparse vector x should satisfy@?@F"x@F"x^+y@?"2^2=