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DIFFERENCE FILTER PRECONDITIONING FOR LARGE COVARIANCE MATRICES

Michael Stein(stein***at***galton.uchicago.edu)
Jie Chen(jiechen***at***mcs.anl.gov)
Mihai Anitescu(anitescu***at***mcs.anl.gov)

Abstract: In many statistical applications one must solve linear systems corresponding to large, dense, and possibly irregularly structured covariance matrices. These matrices are often ill- conditioned; for example, the condition number increases at least linearly with respect to the size of the matrix when observations of a random process are obtained from a xed domain. This paper discusses a preconditioning technique based on a di erencing approach such that the preconditioned covariance matrix has a bounded condition number independent of the size of the matrix for some important process classes. When used in large scale simulations of random processes, signi cant improvement is observed for solving these linear systems with an iterative method.

Keywords: Condition number, preconditioner, stochastic process, random eld, spectral anal- ysis, xed-domain asymptotics

Category 1: Applications -- Science and Engineering (Statistics )

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: Preprint ANL/MCS-P1888-0511

Download: [PDF]

Entry Submitted: 05/19/2011
Entry Accepted: 05/19/2011
Entry Last Modified: 05/19/2011

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