Volume 1 (2) 2007

Title:Properties of Preconditioners for Robust Linear Regression
Authors: Venansius Baryamureeba, Trond Steihaug
Published: ©IJCIR Vol1 (2) 2007, PP. 50-66
Language: English

Abstract:
In this paper, we consider solving the robust linear regression problem y = Ax + E by an inexact Newton method and an iteratively reweighted least squares method. We show that each of these methods can be combined with the preconditioned conjugate gradient least square algorithm to solve large, sparse systems of linear equations efficiently. We consider the constant preconditioner ATA and preconditioners based on low-rank updates and downdates of existing matrix factorizations. Numerical results are given to demonstrate the effectiveness of these preconditioners. View full Article

General Terms: Robust regression, iteratively reweighted least square methods, Newton’s methods, conjugate gradient least squares method, preconditioners
Additional Keywords and Phrases: Low rank updates, matrix factorizations
Categories and Subject Descriptors:G.1.0 [Numerical Analysis]: General-Numerical algorithms; G.1.3 [Numerical Analysis]: numerical Linear Algebra—Conditioning; Linear Systems; Spare, structured and very large systems.

 

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