A Krylov Subspace Method for Covariance Approximation and Simulation of Random Processes and Fields

Authors:
Michael K. Schneider;Alan S. Willsky
Affiliations:
Laboratory for Information and Decision Systems, MIT;Laboratory for Information and Decision Systems, MIT
Venue:
Multidimensional Systems and Signal Processing
Year:
2003

Citing 8
Cited 5

An iterative solution method for solving f(A)x=b, using Krylov subspace information obtained for the symmetric positive definite matrix A

Journal of Computational and Applied Mathematics
Fast Estimation of Principal Eigenspace Using LanczosAlgorithm

SIAM Journal on Matrix Analysis and Applications
Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix

SIAM Journal on Scientific Computing
Applied numerical linear algebra

Applied numerical linear algebra
Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions

SIAM Journal on Matrix Analysis and Applications
Krylov Subspace Estimation

SIAM Journal on Scientific Computing
Internal multiscale autoregressive processes, stochastic realization, and covariance extension

Internal multiscale autoregressive processes, stochastic realization, and covariance extension
Krylov subspace estimation

Krylov subspace estimation

Best approximation of the identity mapping: The case of variable finite memory

Journal of Approximation Theory
Optimal multilinear estimation of a random vector under constraints of causality and limited memory

Computational Statistics & Data Analysis
Generalized consistent estimation on low-rank Krylov subspaces of arbitrarily high dimension

IEEE Transactions on Signal Processing
Original Article: Sparsified Randomization algorithms for low rank approximations and applications to integral equations and inhomogeneous random field simulation

Mathematics and Computers in Simulation
Iterative numerical methods for sampling from high dimensional Gaussian distributions

Statistics and Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper proposes a new iterative algorithm for simultaneously computing an approximation to the covariance matrix of a random vector and drawing a sample from that approximation. The algorithm is especially suited to cases for which the elements of the random vector are samples of a stochastic process or random field. The proposed algorithm has close connections to the conjugate gradient method for solving linear systems of equations. A comparison is made between our algorithm's structure and complexity and other methods for simulation and covariance matrix approximation, including those based on FFTs and Lanczos methods. The convergence of our iterative algorithm is analyzed both analytically and empirically, and a preconditioning technique for accelerating convergence is explored. The numerical examples include a fractional Brownian motion and a random field with the spherical covariance used in geostatistics.