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On the robustness of numerical algorithms for linear systems and signal processing in finite precision arithmetic

This paper proposes a model of the perturbations resulting from finite precision arithmetic implementation of numerical methods. Iterative methods for linear systems are represented as control systems, and the numerical errors caused by finite precision are represented as a multiplicative uncertainty. This representation makes it possible to use results from robust control theory to provide stability criteria, which, in turn, imply convergence, under finite precision arithmetic, of algorithms considered. Numerical examples are taken from several fields in order to illustrate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.