We describe a technique for constructing robust preconditioners for the CGNR method applied to the solution of large and sparse least squares problems. Our algorithm computes an incomplete LDLT factorization of the normal equations matrix without the need to form the normal matrix itself. The preconditioner is reliable (pivot breakdowns cannot occur) and has low intermediate storage requirements. Numerical experiments illustrating the performance of the preconditioner are presented.
Key words: Large sparse least squares problems, preconditioned CGNR, robust incomplete factorization, incomplete C-orthogonalization
AMS subject classifications: Primary 65F10, 65F20, 65F25, 65F35, 65F50. Secondary 15A06.