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Michael Stein(steingalton.uchicago.edu) 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 dierencing 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, signicant improvement is observed for solving these linear systems with an iterative method. Keywords: Condition number, preconditioner, stochastic process, random eld, spectral anal ysis, xeddomain asymptotics Category 1: Applications  Science and Engineering (Statistics ) Category 2: Nonlinear Optimization (Unconstrained Optimization ) Citation: Preprint ANL/MCSP18880511 Download: [PDF] Entry Submitted: 05/19/2011 Modify/Update this entry  
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