@article{Hasan:2012:10.1109/TAC.2012.2225513,
author = {Hasan, A and Kerrigan, EC and Constantinides, GA},
doi = {10.1109/TAC.2012.2225513},
journal = {IEEE Transactions on Automatic Control},
pages = {1524--1529},
title = {Control-theoretic forward error analysis of iterative numericalalgorithms},
url = {http://dx.doi.org/10.1109/TAC.2012.2225513},
volume = {58},
year = {2012}
}

Download

TY  - JOUR
AB  - It has been known for at least five decades that control theorycan be used to study iterative algorithms. However, little work can be foundin the control systems literature on numerical algorithms, especially on thestudy of finite precision effects. In this technical note, we consider numericaliterative algorithms in finite precision as dynamical systems and studythe effects of finite precision using control theory. By using the control toolsof input-to-state stability and results from the study of quantization in controlsystems, we present new systematic ways to find bounds on the forwarderror for iterative algorithms. The advantages of the proposed schemes areshown by applying them to find bounds for the classical iterative methodsfor solving a system of linear equations.
AU  - Hasan,A
AU  - Kerrigan,EC
AU  - Constantinides,GA
DO  - 10.1109/TAC.2012.2225513
EP  - 1529
PY  - 2012///
SN  - 0018-9286
SP  - 1524
TI  - Control-theoretic forward error analysis of iterative numericalalgorithms
T2  - IEEE Transactions on Automatic Control
UR  - http://dx.doi.org/10.1109/TAC.2012.2225513
UR  - http://hdl.handle.net/10044/1/26452
VL  - 58
ER  - 

Download