Flavio Chierichetti, Sreenivas Gollapudi, Ravi Kumar, Silvio Lattanzi, Rina Panigrahy, David
We consider the problem of approximating a given matrix by a low-rank matrix so as
to minimize the entrywise ℓp-approximation error, for any p≥1; the case p=2 is the
classical SVD problem. We obtain the first provably good approximation algorithms
for this version of low-rank approximation that work for every value of p≥1,
including p=∞. Our algorithms are simple, easy to implement, work well in practice,
and illustrate interesting tradeoffs between the approximation quality, the running
time, and the rank of the approximating matrix.