Algorithm 853: An efficient algorithm for solving rank-deficient least squares problems
Existing routines, such as xGELSY or xGELSD in LAPACK, for solving rank-deficient least squares problems require O(mn(2)) operations to solve min parallel to b-Ax parallel to where A is an m b y n matrix. We present a modification of the LAPACK routine xGELSY that requires O(mnk) operations where k is the effective numerical rank of the matrix A. For low rank matrices the modification is an order of magnitude faster than the LAPACK code.
algorithms rank-deficient least squares performance qr factorization