Incomplete hyperbolic Gram–Schmidt-based preconditioners for the solution of large indefinite least squares problems

摘要

We propose to precondition the CGILS method based on the incomplete hyperbolic Gram–Schmidt methods for the solution of the large and sparse indefinite least squares (ILS) problem, which requires minimization of an indefinite quadratic form. Numerical experiments show that the incomplete hyperbolic classical/modified Gram–Schmidt (IHCGS/IHMGS) preconditioners can generally greatly reduce the number of iterations, and IHMGS has a better quality for ill-conditioned problems but may be expensive in computation cost.