NII Technical Report (NII-2007-008E)

Title Preconditioned GMRES Methods with Incomplete Givens Orthogonalization Method for Large Sparse Least-Squares Problem
Authors Jun-Feng Yin and Ken Hayami
Abstract 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.
Language English
Published Jul 9, 2007
Pages 18p

NII Technical Reports
National Institute of Informatics