A Deflated Version of the Block Conjugate Gradient Algorithm with an Application to Gaussian Process Maximum Likelihood Estimation

TitleA Deflated Version of the Block Conjugate Gradient Algorithm with an Application to Gaussian Process Maximum Likelihood Estimation
Publication TypeJournal Article
Year of Publication2011
AuthorsChen, J
JournalSIAM J. Matrix Anal. Appl.
Other NumbersANL/MCS-P1927-0811
Abstract

Many statistical applications require the solution of a symmetric positive denite covariance matrix, sometimes with a large number of right-hand sides of a statistical independence nature. With preconditioning, the preconditioned matrix has almost all the eigenvalues clustered within a narrow range, except for a few extreme eigenvalues deviating from the range rapidly. We derive a deflated version of the block conjugate gradient algorithm to handle the extreme eigenvalues and the multiple right-hand sides. With an appropriate deflation, the rate of convergence depends on the spread of the clustered eigenvalues but not the extreme ones. Numerical experiments in a Gaussian process maximum likelihood estimation application demonstrate the effectiveness of the proposed solver, pointing to the potential of solving very large scale, real-life data analysis problems.

PDFhttp://www.mcs.anl.gov/papers/P1927-0811.pdf