Some applications of the rank revealing QR factorization
SIAM Journal on Scientific and Statistical Computing
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
Tikhonov Regularization and Total Least Squares
SIAM Journal on Matrix Analysis and Applications
Algorithms for simultaneous sparse approximation: part I: Greedy pursuit
Signal Processing - Sparse approximations in signal and image processing
Algorithms for simultaneous sparse approximation: part II: Convex relaxation
Signal Processing - Sparse approximations in signal and image processing
An improved approximation algorithm for the column subset selection problem
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Near Optimal Column-Based Matrix Reconstruction
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
| Hi-index | 0.89 |
We compute a sparse solution to the classical least-squares problem min"x@?Ax-b@?"2, where A is an arbitrary matrix. We describe a novel algorithm for this sparse least-squares problem. The algorithm operates as follows: first, it selects columns from A, and then solves a least-squares problem only with the selected columns. The column selection algorithm that we use is known to perform well for the well studied column subset selection problem. The contribution of this article is to show that it gives favorable results for sparse least-squares as well. Specifically, we prove that the solution vector obtained by our algorithm is close to the solution vector obtained via what is known as the ''SVD-truncated regularization approach''.