||We propose to precondition the GMRES method by using the
incomplete Givens orthogonalization (IGO) method
for the solution of large sparse linear least-squares problems.
Theoretical analysis shows that the preconditioner satisfies the sufficient condition that can guarantee that the preconditioned GMRES method will never break down and always give the least-squares solution of the original problem.
Numerical experiments further confirm that the new peconditioner is efficient and the preconditioned GMRES method is faster than the CGLS, LSQR and reorthogonalized CGLS (RCGLS) methods incorporated also with the IGO preconditioner.
Detailed comparisons of IGO and RIF preconditioners are also addressed.