Title :
A Krylov subspace method for large estimation problems
Author :
Schneider, Michael K. ; Willsky, Alan S.
Author_Institution :
Lab. for Inf. & Decision Syst., MIT, Cambridge, MA, USA
Abstract :
Computing the linear least-squares estimate of a high-dimensional random quantity given noisy data requires solving a large system of linear equations. In many situations, one can solve this system efficiently using the conjugate gradient (CG) algorithm. Computing the estimation error variances is a more intricate task. It is difficult because the error variances are the diagonal elements of a complicated matrix. This paper presents a method for using the conjugate search directions generated by the CG algorithm to obtain a converging approximation to the estimation error variances. The algorithm for computing the error variances falls out naturally from a novel estimation-theoretic interpretation of the CG algorithm. The paper discusses this interpretation and convergence issues and presents numerical examples
Keywords :
conjugate gradient methods; convergence of numerical methods; error analysis; estimation theory; least squares approximations; matrix algebra; noise; random processes; search problems; Krylov subspace method; conjugate gradient algorithm; conjugate search directions; converging approximation; estimation error variances; estimation-theoretic interpretation; high-dimensional random quantity; large estimation problems; linear equation; linear least-squares estimate; matrix; noisy data; numerical examples; Approximation algorithms; Biomedical imaging; Character generation; Convergence of numerical methods; Covariance matrix; Data analysis; Equations; Estimation error; Laboratories; Remote sensing;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5041-3
DOI :
10.1109/ICASSP.1999.756321
