Neighborly Polytopes and Sparse Solution of Underdetermined Linear Equations

  title={Neighborly Polytopes and Sparse Solution of Underdetermined Linear Equations},
  author={David L. Donoho},
Consider a d × n matrix A, with d < n. The problem of solving for x in y = Ax is underdetermined, and has many possible solutions (if there are any). In several fields it is of interest to find the sparsest solution – the one with fewest nonzeros – but in general this involves combinatorial optimization. Let ai denote the i-th column of A, 1 ≤ i ≤ n. Associate to A the quotient polytope P formed by taking the convex hull of the 2n points (±ai) in R. P is centrosymmetric and is called (centrally… CONTINUE READING
Highly Influential
This paper has highly influenced a number of papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 318 citations. REVIEW CITATIONS

1 Figure or Table



Citations per Year

318 Citations

Semantic Scholar estimates that this publication has 318 citations based on the available data.

See our FAQ for additional information.