A fast randomized algorithm for overdetermined linear least-squares regression.
We introduce a randomized algorithm for overdetermined linear least-squares regression. Given an arbitrary full-rank m x n matrix A with m >/= n, any m x 1 vector b, and any positive real number epsilon, the procedure computes an n x 1 vector x such that x minimizes the Euclidean norm ||Ax - b || to relative precision epsilon. The algorithm typically requires ((log(n)+log(1/epsilon))mn+n(3)) floating-point operations. This cost is less than the (mn(2)) required by the classical schemes based on QR-decompositions or bidiagonalization. We present several numerical examples illustrating the performance of the algorithm.
Rokhlin
Vladimir
V
Program in Applied Mathematics, Yale University, A. K. Watson Hall, 51 Prospect Street, New Haven, CT 06511, USA.
Tygert
Mark
M
D000465:Algorithms; D016018:Least-Squares Analysis; D016014:Linear Models
Proc Natl Acad Sci U S A. 2007 Dec 18;104(51):20167-72
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