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Difference filter preconditioning for large covariance matrices. (English) Zbl 1251.65043

In many statistical applications one must solve linear systems involving large, dense, and possibly irregularly structured covariance matrices. These matrices are often ill-conditioned. This paper discusses a preconditioning technique based on a differencing approach such that the preconditioned covariance matrix has a bounded condition number independent of the size of the matrix for some important process classes. It is shown that significant improvement is observed for solving these linear systems with an iterative method when used in large scale simulations of random processes.

MSC:

65F08 Preconditioners for iterative methods
65F35 Numerical computation of matrix norms, conditioning, scaling
60G25 Prediction theory (aspects of stochastic processes)
62M15 Inference from stochastic processes and spectral analysis
62J10 Analysis of variance and covariance (ANOVA)
60G60 Random fields

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