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Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/5598
Title: Accurate Solution of Weighted Least Squares by Iterative Methods
Authors: Bobrovnikova, Elena Y.
Vavasis, Stephen A.
Keywords: theory center
Issue Date: 6-Feb-1997
Publisher: Cornell University
Citation: http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.tc/97-268
Abstract: We 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.
URI: http://hdl.handle.net/1813/5598
Appears in Collections:Cornell Theory Center Technical Reports

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