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|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|
|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.|
|Appears in Collections:||Cornell Theory Center Technical Reports|
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