Bobrovnikova, Elena Y.Vavasis, Stephen A.2007-04-042007-04-041997-02-06http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.tc/97-268https://hdl.handle.net/1813/5598We consider the weighted least-squares (WLS) problem with a very ill-conditioned weight matrix. Weighted least-squares problems arise in many applications including linear programming, electrical networks, boundary value problems, and structures. Because of roundoff errors, standard iterative methods for solving a WLS problem with ill-conditioned weights may not give the correct answer. Indeed, the difference between the true and computed solution (forward error) may be large. We propose an iterative algorithm, called MINRES-L, for solving WLS problems. The MINRES-L method is the application of MINRES, a Krylov-space method due to Paige and Saunders, to a certain layered linear system. Using a simplified model of the effects of round off error, we prove that MINRES-L gives answers with small forward error. We present computational experiments for some applications.419229 bytes350056 bytesapplication/pdfapplication/postscripten-UStheory centertechnical report