Difference Filter Preconditioning for Large Covariance Matrices

Authors:
Michael L. Stein;Jie Chen;Mihai Anitescu
Affiliations:
stein@galton.uchicago.edu;jiechen@mcs.anl.gov and anitescu@mcs.anl.gov;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2012

Citing 6
Cited 0

A fast algorithm for particle simulations

Journal of Computational Physics
Gaussian Markov Random Fields: Theory And Applications (Monographs on Statistics and Applied Probability)

Gaussian Markov Random Fields: Theory And Applications (Monographs on Statistics and Applied Probability)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)

Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Fast Radial Basis Function Interpolation via Preconditioned Krylov Iteration

SIAM Journal on Scientific Computing
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)

An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix

Journal of the ACM (JACM)

Quantified Score

Hi-index	0.00

Visualization

Abstract

In many statistical applications one must solve linear systems involving 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 fixed domain. 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. When used in large scale simulations of random processes, significant improvement is observed for solving these linear systems with an iterative method.