Sparse Approximate Solutions to Linear Systems

  title={Sparse Approximate Solutions to Linear Systems},
  author={Balas K. Natarajan},
  journal={SIAM J. Comput.},
  • B. Natarajan
  • Published 1 April 1995
  • Mathematics, Computer Science
  • SIAM J. Comput.
The following problem is considered: given a matrix $A$ in ${\bf R}^{m \times n}$, ($m$ rows and $n$ columns), a vector $b$ in ${\bf R}^m$, and ${\bf \epsilon} > 0$, compute a vector $x$ satisfying $\| Ax - b \|_2 \leq {\bf \epsilon}$ if such exists, such that $x$ has the fewest number of non-zero entries over all such vectors. It is shown that the problem is NP-hard, but that the well-known greedy heuristic is good in that it computes a solution with at most $\left\lceil 18 \mbox{ Opt} ({\bf… Expand
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