Algorithms for Block Tridiagonal Systems: Stability Results for Generalized Kalman Smoothing. Issue 7 (2021)

• Record Type: Journal Article
• Authors: Aravkin, Aleksandr Y.; Burke, James V.; Bell, Bradley M.; Pillonetto, Gianluigi
• Is Part Of: IFAC-PapersOnLine. Volume 54:Issue 7(2021)
• Page Start: 821
• Page End: 826
• Publication Date: 2021
• Subjects: generalized Kalman smoothing -- linear algebra -- numerical stability -- optimization; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.08.463
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: Block tridiagonal systems appear in classic Kalman smoothing problems, as well in generalized Kalman smoothing, where problems may have nonsmooth terms, singular covariance, constraints, nonlinear models, and unknown parameters. In this paper, first we interpret all the classic smoothing algorithms as different approaches to solve positive definite block tridiagonal linear systems. Then, we obtain new results on their numerical stability. Our outcomes apply to all systems with dynamic structure, informing both classic and modern inference for generalized Kalman smoothing.